We investigate the optimal model reduction problem for large-scale quadratic-bilinear (QB) control systems. Our contributions are threefold. First, we discuss the variational analysis and the Volterra series formulation for QB systems. We then define the $\mathcal H_2$-norm for a QB system based on the kernels of the underlying Volterra series and also propose a truncated $\mathcal H_2$-norm. Next, we derive first-order necessary conditions for an optimal approximation, where optimality is measured in term of the truncated $\mathcal H_2$-norm of the error system. We then propose an iterative model reduction algorithm, which upon convergence yields a reduced-order system that approximately satisfies the newly derived optimality conditions. We also discuss an efficient computation of the reduced Hessian, using the special Kronecker structure of the Hessian of the system. We illustrate the efficiency of the proposed method by means of several numerical examples resulting from semi-discretized nonlinear partial differential equations and show its competitiveness with the existing model reduction schemes for QB systems such as moment-matching methods and balanced truncation.
Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily focus on an operator inference methodology that builds dynamical models, preferably in low-dimension, with a prior hypothesis on the model structure, often determined by known physics or given by experts. Then, for inference, we aim to learn the operators of a model by setting up an appropriate optimization problem. One of the critical properties of dynamical systems is stability. However, this property is not guaranteed by the inferred models. In this work, we propose inference formulations to learn quadratic models, which are stable by design. Precisely, we discuss the parameterization of quadratic systems that are locally and globally stable. Moreover, for quadratic systems with no stable point yet bounded (e.g., chaotic Lorenz model), we discuss how to parameterize such bounded behaviors in the learning process. Using those parameterizations, we set up inference problems, which are then solved using a gradient-based optimization method. Furthermore, to avoid numerical derivatives and still learn continuous systems, we make use of an integral form of differential equations. We present several numerical examples, illustrating the preservation of stability and discussing its comparison with the existing state-of-the-art approach to infer operators. By means of numerical examples, we also demonstrate how the proposed methods are employed to discover governing equations and energy-preserving models.
NLP in the legal domain has seen increasing success with the emergence of Transformer-based Pre-trained Language Models (PLMs) pre-trained on legal text. PLMs trained over European and US legal text are available publicly; however, legal text from other domains (countries), such as India, have a lot of distinguishing characteristics. With the rapidly increasing volume of Legal NLP applications in various countries, it has become necessary to pre-train such LMs over legal text of other countries as well. In this work, we attempt to investigate pre-training in the Indian legal domain. We re-train (continue pre-training) two popular legal PLMs, LegalBERT and CaseLawBERT, on Indian legal data, as well as train a model from scratch with a vocabulary based on Indian legal text. We apply these PLMs over three benchmark legal NLP tasks -- Legal Statute Identification from facts, Semantic Segmentation of Court Judgment Documents, and Court Appeal Judgment Prediction -- over both Indian and non-Indian (EU, UK) datasets. We observe that our approach not only enhances performance on the new domain (Indian texts) but also over the original domain (European and UK texts). We also conduct explainability experiments for a qualitative comparison of all these different PLMs.
The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for modeling the dynamics of nonlinear systems. To simplify this task, we aim to identify a coordinate transformation that allows us to represent the dynamics of nonlinear systems using a common, simple model structure. The advantage of a common simple model is that customized design tools developed for it can be applied to study a large variety of nonlinear systems. The simplest common model -- one can think of -- is linear, but linear systems often fall short in accurately capturing the complex dynamics of nonlinear systems. In this work, we propose using quadratic systems as the common structure, inspired by the lifting principle. According to this principle, smooth nonlinear systems can be expressed as quadratic systems in suitable coordinates without approximation errors. However, finding these coordinates solely from data is challenging. Here, we leverage deep learning to identify such lifted coordinates using only data, enabling a quadratic dynamical system to describe the system's dynamics. Additionally, we discuss the asymptotic stability of these quadratic dynamical systems. We illustrate the approach using data collected from various numerical examples, demonstrating its superior performance with the existing well-known techniques.
In recent years, graph neural network (GNN) based approaches have emerged as a powerful technique to encode complex topological structure of crystal materials in an enriched representation space. These models are often supervised in nature and using the property-specific training data, learn relationship between crystal structure and different properties like formation energy, bandgap, bulk modulus, etc. Most of these methods require a huge amount of property-tagged data to train the system which may not be available for different properties. However, there is an availability of a huge amount of crystal data with its chemical composition and structural bonds. To leverage these untapped data, this paper presents CrysGNN, a new pre-trained GNN framework for crystalline materials, which captures both node and graph level structural information of crystal graphs using a huge amount of unlabelled material data. Further, we extract distilled knowledge from CrysGNN and inject into different state of the art property predictors to enhance their property prediction accuracy. We conduct extensive experiments to show that with distilled knowledge from the pre-trained model, all the SOTA algorithms are able to outperform their own vanilla version with good margins. We also observe that the distillation process provides a significant improvement over the conventional approach of finetuning the pre-trained model. We have released the pre-trained model along with the large dataset of 800K crystal graph which we carefully curated; so that the pretrained model can be plugged into any existing and upcoming models to enhance their prediction accuracy.
Machine Learning models have emerged as a powerful tool for fast and accurate prediction of different crystalline properties. Exiting state-of-the-art models rely on a single modality of crystal data i.e. crystal graph structure, where they construct multi-graph by establishing edges between nearby atoms in 3D space and apply GNN to learn materials representation. Thereby, they encode local chemical semantics around the atoms successfully but fail to capture important global periodic structural information like space group number, crystal symmetry, rotational information, etc, which influence different crystal properties. In this work, we leverage textual descriptions of materials to model global structural information into graph structure and learn a more robust and enriched representation of crystalline materials. To this effect, we first curate a textual dataset for crystalline material databases containing descriptions of each material. Further, we propose CrysMMNet, a simple multi-modal framework, which fuses both structural and textual representation together to generate a joint multimodal representation of crystalline materials. We conduct extensive experiments on two benchmark datasets across ten different properties to show that CrysMMNet outperforms existing state-of-the-art baseline methods with a good margin. We also observe that fusing the textual representation with crystal graph structure provides consistent improvement for all the SOTA GNN models compared to their own vanilla versions. We have shared the textual dataset, that we have curated for both the benchmark material databases, with the community for future use.
Süleyman Yildiz, Pawan Goyal, Thomas Bendokat et al.
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system. To that end, for given generalized position and momentum data, we propose a methodology to learn quadratic dynamical systems, enforcing the Hamiltonian structure in combination with a weakly-enforced symplectic auto-encoder. The obtained Hamiltonian structure exhibits long-term stability of the system, while the cubic Hamiltonian function provides relatively low model complexity. For low-dimensional data, we determine a higher-dimensional transformed coordinate system, whereas for high-dimensional data, we find a lower-dimensional coordinate system with the desired properties. We demonstrate the proposed methodology by means of both low-dimensional and high-dimensional nonlinear Hamiltonian systems.
Causality represents the foremost relation between events in financial documents such as financial news articles, financial reports. Each financial causality contains a cause span and an effect span. Previous works proposed sequence labeling approaches to solve this task. But sequence labeling models find it difficult to extract multiple causalities and overlapping causalities from the text segments. In this paper, we explore a generative approach for causality extraction using the encoder-decoder framework and pointer networks. We use a causality dataset from the financial domain, \textit{FinCausal}, for our experiments and our proposed framework achieves very competitive performance on this dataset.
Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We discuss a methodology to learn differential equation(s) using noisy and irregular sampled measurements. In our methodology, the main innovation can be seen in the integration of deep neural networks with the neural ordinary differential equations (ODEs) approach. Precisely, we aim at learning a neural network that provides (approximately) an implicit representation of the data and an additional neural network that models the vector fields of the dependent variables. We combine these two networks by constraining using neural ODEs. The proposed framework to learn a model describing the vector field is highly effective under noisy measurements. The approach can handle scenarios where dependent variables are not available at the same temporal grid. Moreover, a particular structure, e.g., second-order with respect to time, can easily be incorporated. We demonstrate the effectiveness of the proposed method for learning models using data obtained from various differential equations and present a comparison with the neural ODE method that does not make any special treatment to noise.
Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers a framework for global linearization for nonlinear systems, thereby allowing the usage of linear tools for design studies. In this work, we focus on the identification of global linearized embeddings for canonical nonlinear Hamiltonian systems through a symplectic transformation. While this task is often challenging, we leverage the power of deep learning to discover the desired embeddings. Furthermore, to overcome the shortcomings of Koopman operators for systems with continuous spectra, we apply the lifting principle and learn global cubicized embeddings. Additionally, a key emphasis is paid to enforce the bounded stability for the dynamics of the discovered embeddings. We demonstrate the capabilities of deep learning in acquiring compact symplectic coordinate transformation and the corresponding simple dynamical models, fostering data-driven learning of nonlinear canonical Hamiltonian systems, even those with continuous spectra.
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is especially important in design tasks such as prediction and control. Thus, there is a need to develop methodologies that provide stability guarantees. To that end, we leverage the parameterization of stable matrices proposed in [Gillis/Sharma, Automatica, 2017] to realize the desired models. Furthermore, to avoid the estimation of derivative information to learn continuous systems, we formulate the inference problem in an integral form. We also discuss a few extensions, including those related to control systems. Numerical experiments show that the combination of a stable matrix parameterization and an integral form of differential equations allows us to learn stable systems without requiring derivative information, which can be challenging to obtain in situations with noisy or limited data.
We discuss model reduction for a particular class of quadratic-bilinear (QB) descriptor systems. The main goal of this article is to extend the recently studied interpolation-based optimal model reduction framework for QBODEs [Benner et al. '16] to a class of descriptor systems in an efficient and reliable way. Recently, it has been shown in the case of linear or bilinear systems that a direct extension of interpolation-based model reduction techniques to descriptor systems, without any modifications, may lead to poor reduced-order systems. Therefore, for the analysis, we aim at transforming the considered QB descriptor system into an equivalent QBODE system by means of projectors for which standard model reduction techniques for QBODEs can be employed, including aforementioned interpolation scheme. Subsequently, we discuss related computational issues, thus resulting in a modified algorithm that allows us to construct \emph{near}--optimal reduced-order systems without explicitly computing the projectors used in the analysis. The efficiency of the proposed algorithm is illustrated by means of a numerical example, obtained via semi-discretization of the Navier-Stokes equations.
The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and scarce data still pose a severe challenge to the success of the SINDy approach. In this work, we discuss a robust method to discover nonlinear governing equations from noisy and scarce data. To do this, we make use of neural networks to learn an implicit representation based on measurement data so that not only it produces the output in the vicinity of the measurements but also the time-evolution of output can be described by a dynamical system. Additionally, we learn such a dynamic system in the spirit of the SINDy framework. Leveraging the implicit representation using neural networks, we obtain the derivative information -- required for SINDy -- using an automatic differentiation tool. To enhance the robustness of our methodology, we further incorporate an integral condition on the output of the implicit networks. Furthermore, we extend our methodology to handle data collected from multiple initial conditions. We demonstrate the efficiency of the proposed methodology to discover governing equations under noisy and scarce data regimes by means of several examples and compare its performance with existing methods.
Mohammad S. Khorrami, Pawan Goyal, Jaber R. Mianroodi et al.
The purpose of the current work is the development of a so-called physics-encoded Fourier neural operator (PeFNO) for surrogate modeling of the quasi-static equilibrium stress field in solids. Rather than accounting for constraints from physics in the loss function as done in the (now standard) physics-informed approach, the physics-encoded approach incorporates or "encodes" such constraints directly into the network or operator architecture. As a result, in contrast to the physics-informed approach in which only training is physically constrained, both training and output are physically constrained in the physics-encoded approach. For the current constraint of divergence-free stress, a novel encoding approach based on a stress potential is proposed. As a "proof-of-concept" example application of the proposed PeFNO, a heterogeneous polycrystalline material consisting of isotropic elastic grains subject to uniaxial extension is considered. Stress field data for training are obtained from the numerical solution of a corresponding boundary-value problem for quasi-static mechanical equilibrium. This data is also employed to train an analogous physics-guided FNO (PgFNO) and physics-informed FNO (PiFNO) for comparison. As confirmed by this comparison and as expected on the basis of their differences, the output of the trained PeFNO is significantly more accurate in satisfying mechanical equilibrium than the output of either the trained PgFNO or the trained PiFNO.
Interdisciplinarity has over the recent years have gained tremendous importance and has become one of the key ways of doing cutting edge research. In this paper we attempt to model the citation flow across three different fields -- Physics (PHY), Mathematics (MA) and Computer Science (CS). For instance, is there a specific pattern in which these fields cite one another? We carry out experiments on a dataset comprising more than 1.2 million articles taken from these three fields. We quantify the citation interactions among these three fields through temporal bucket signatures. We present numerical models based on variants of the recently proposed relay-linking framework to explain the citation dynamics across the three disciplines. These models make a modest attempt to unfold the underlying principles of how citation links could have been formed across the three fields over time.
This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving reduced-order methods use symplectic Galerkin projection to construct reduced-order Hamiltonian models by projecting the full models onto a symplectic subspace. However, symplectic projection requires the existence of fully discrete operators, and in many cases, such as black-box PDE solvers, these operators are inaccessible. In this work, we propose an energy-preserving machine learning method that can infer the dynamics of the given PDE using data only, so that the proposed framework does not depend on the fully discrete operators. In this context, the proposed method is non-intrusive. The proposed method is grey box in the sense that it requires only some basic knowledge of the multi-symplectic model at the partial differential equation level. We prove that the proposed method satisfies spatially discrete local energy conservation and preserves the multi-symplectic conservation laws. We test our method on the linear wave equation, the Korteweg-de Vries equation, and the Zakharov-Kuznetsov equation. We test the generalization of our learned models by testing them far outside the training time interval.
Celine Reddig, Pawan Goyal, Igor Pontes Duff et al.
Model reduction is an active research field to construct low-dimensional surrogate models of high fidelity to accelerate engineering design cycles. In this work, we investigate model reduction for linear structured systems using dominant reachable and observable subspaces. When the training set $-$ containing all possible interpolation points $-$ is large, then these subspaces can be determined by solving many large-scale linear systems. However, for high-fidelity models, this easily becomes computationally intractable. To circumvent this issue, in this work, we propose an active sampling strategy to sample only a few points from the given training set, which can allow us to estimate those subspaces accurately. To this end, we formulate the identification of the subspaces as the solution of the generalized Sylvester equations, guiding us to select the most relevant samples from the training set to achieve our goals. Consequently, we construct solutions of the matrix equations in low-rank forms, which encode subspace information. We extensively discuss computational aspects and efficient usage of the low-rank factors in the process of obtaining reduced-order models. We illustrate the proposed active sampling scheme to obtain reduced-order models via dominant reachable and observable subspaces and present its comparison with the method where all the points from the training set are taken into account. It is shown that the active sample strategy can provide us $17$x speed-up without sacrificing any noticeable accuracy.
The task of Legal Statute Identification (LSI) aims to identify the legal statutes that are relevant to a given description of Facts or evidence of a legal case. Existing methods only utilize the textual content of Facts and legal articles to guide such a task. However, the citation network among case documents and legal statutes is a rich source of additional information, which is not considered by existing models. In this work, we take the first step towards utilising both the text and the legal citation network for the LSI task. We curate a large novel dataset for this task, including Facts of cases from several major Indian Courts of Law, and statutes from the Indian Penal Code (IPC). Modeling the statutes and training documents as a heterogeneous graph, our proposed model LeSICiN can learn rich textual and graphical features, and can also tune itself to correlate these features. Thereafter, the model can be used to inductively predict links between test documents (new nodes whose graphical features are not available to the model) and statutes (existing nodes). Extensive experiments on the dataset show that our model comfortably outperforms several state-of-the-art baselines, by exploiting the graphical structure along with textual features. The dataset and our codes are available at https://github.com/Law-AI/LeSICiN.
Kishalay Das, Subhojyoti Khastagir, Pawan Goyal et al.
Equivariant diffusion models have emerged as the prevailing approach for generating novel crystal materials due to their ability to leverage the physical symmetries of periodic material structures. However, current models do not effectively learn the joint distribution of atom types, fractional coordinates, and lattice structure of the crystal material in a cohesive end-to-end diffusion framework. Also, none of these models work under realistic setups, where users specify the desired characteristics that the generated structures must match. In this work, we introduce TGDMat, a novel text-guided diffusion model designed for 3D periodic material generation. Our approach integrates global structural knowledge through textual descriptions at each denoising step while jointly generating atom coordinates, types, and lattice structure using a periodic-E(3)-equivariant graph neural network (GNN). Extensive experiments using popular datasets on benchmark tasks reveal that TGDMat outperforms existing baseline methods by a good margin. Notably, for the structure prediction task, with just one generated sample, TGDMat outperforms all baseline models, highlighting the importance of text-guided diffusion. Further, in the generation task, TGDMat surpasses all baselines and their text-fusion variants, showcasing the effectiveness of the joint diffusion paradigm. Additionally, incorporating textual knowledge reduces overall training and sampling computational overhead while enhancing generative performance when utilizing real-world textual prompts from experts.
Subhendu Khatuya, Koushiki Sinha, Niloy Ganguly et al.
While automatic summarization techniques have made significant advancements, their primary focus has been on summarizing short news articles or documents that have clear structural patterns like scientific articles or government reports. There has not been much exploration into developing efficient methods for summarizing financial documents, which often contain complex facts and figures. Here, we study the problem of bullet point summarization of long Earning Call Transcripts (ECTs) using the recently released ECTSum dataset. We leverage an unsupervised question-based extractive module followed by a parameter efficient instruction-tuned abstractive module to solve this task. Our proposed model FLAN-FinBPS achieves new state-of-the-art performances outperforming the strongest baseline with 14.88% average ROUGE score gain, and is capable of generating factually consistent bullet point summaries that capture the important facts discussed in the ECTs.
Subhendu Khatuya, Rajdeep Mukherjee, Akash Ghosh et al.
We study the problem of automatically annotating relevant numerals (GAAP metrics) occurring in the financial documents with their corresponding XBRL tags. Different from prior works, we investigate the feasibility of solving this extreme classification problem using a generative paradigm through instruction tuning of Large Language Models (LLMs). To this end, we leverage metric metadata information to frame our target outputs while proposing a parameter efficient solution for the task using LoRA. We perform experiments on two recently released financial numeric labeling datasets. Our proposed model, FLAN-FinXC, achieves new state-of-the-art performances on both the datasets, outperforming several strong baselines. We explain the better scores of our proposed model by demonstrating its capability for zero-shot as well as the least frequently occurring tags. Also, even when we fail to predict the XBRL tags correctly, our generated output has substantial overlap with the ground-truth in majority of the cases.
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability is a fundamental attribute of dynamical systems, yet it is not always assured in models derived through inference. Our main objective is to develop a method that facilitates the inference of quadratic control dynamical systems with inherent stability guarantees. To this aim, we investigate the stability characteristics of control systems with energy-preserving nonlinearities, thereby identifying conditions under which such systems are bounded-input bounded-state stable. These insights are subsequently applied to the learning process, yielding inferred models that are inherently stable by design. The efficacy of our proposed framework is demonstrated through a couple of numerical examples.
Ion Victor Gosea, Luisa Peterson, Pawan Goyal et al.
In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This is a non-intrusive, data-driven method for learning dynamical systems from time-domain data. The application in our study is carbon dioxide methanation, an important reaction within the Power-to-X framework, to demonstrate its potential. The numerical results show the ability of the reduced-order models constructed with operator inference to provide a reduced yet accurate surrogate solution. This represents an important milestone towards the implementation of fast and reliable digital twin architectures.
In this paper, we introduce Spotlight, a novel paradigm for information extraction that produces concise, engaging narratives by highlighting the most compelling aspects of a document. Unlike traditional summaries, which prioritize comprehensive coverage, spotlights selectively emphasize intriguing content to foster deeper reader engagement with the source material. We formally differentiate spotlights from related constructs and support our analysis with a detailed benchmarking study using new datasets curated for this work. To generate high-quality spotlights, we propose a two-stage approach: fine-tuning a large language model on our benchmark data, followed by alignment via Direct Preference Optimization (DPO). Our comprehensive evaluation demonstrates that the resulting model not only identifies key elements with precision but also enhances readability and boosts the engagement value of the original document.
Standard language models employ unique, monolithic embeddings for each token, potentially limiting their ability to capture the multifaceted nature of word meanings. We investigate whether tokens can be more effectively represented through a compositional structure that accumulates diverse semantic facets. To explore this, we propose Aggregate Semantic Grouping (ASG), a novel approach leveraging Product Quantization (PQ). We apply ASG to standard transformer architectures (mBERT, XLM-R, mT5) and evaluate this representational scheme across diverse tasks (NLI, NER, QA), as well as a biomedical domain-specific benchmark (BC5CDR) using BioBERT. Our findings demonstrate that representing tokens compositionally via ASG achieves extreme compression in embedding parameters (0.4--0.5\%) while maintaining $>$95\% task performance relative to the base model, even in generative tasks and extends to both cross lingual transfer and domain-specific settings. These results validate the principle that tokens can be effectively modeled as combinations of shared semantic building blocks. ASG offers a simple yet concrete method for achieving this, showcasing how compositional representations can capture linguistic richness while enabling compact yet semantically rich models.
Sandeep Mishra, Anubhab Mandal, Bishal Santra et al.
Ghosting, the ability to predict a user's intended text input for inline query auto-completion, is an invaluable feature for modern search engines and chat interfaces, greatly enhancing user experience. By suggesting completions to incomplete queries (or prefixes), ghosting aids users with slow typing speeds, disabilities, or limited language proficiency. Ghosting is a challenging problem and has become more important with the ubiquitousness of chat-based systems like ChatGPT, Copilot, etc. Despite the increasing prominence of chat-based systems utilizing ghosting, this challenging problem of Chat-Ghosting has received little attention from the NLP/ML research community. There is a lack of standardized benchmarks and relative performance analysis of deep learning and non-deep learning methods. We address this through an open and thorough study of this problem using four publicly available dialog datasets: two human-human (DailyDialog and DSTC7-Ubuntu) and two human-bot (Open Assistant and ShareGPT). We experiment with various existing query auto-completion methods (using tries), n-gram methods and deep learning methods, with and without dialog context. We also propose a novel entropy-based dynamic early stopping strategy. Our analysis finds that statistical n-gram models and tries outperform deep learning based models in terms of both model performance and inference efficiency for seen prefixes. For unseen queries, neural models like T5 and Phi-2 lead to better results. Adding conversational context leads to significant improvements in ghosting quality, especially for Open-Assistant and ShareGPT. We make code and data publicly available
Rajdeep Mukherjee, Uppada Vishnu, Hari Chandana Peruri et al.
Occurrences of catastrophes such as natural or man-made disasters trigger the spread of rumours over social media at a rapid pace. Presenting a trustworthy and summarized account of the unfolding event in near real-time to the consumers of such potentially unreliable information thus becomes an important task. In this work, we propose MTLTS, the first end-to-end solution for the task that jointly determines the credibility and summary-worthiness of tweets. Our credibility verifier is designed to recursively learn the structural properties of a Twitter conversation cascade, along with the stances of replies towards the source tweet. We then take a hierarchical multi-task learning approach, where the verifier is trained at a lower layer, and the summarizer is trained at a deeper layer where it utilizes the verifier predictions to determine the salience of a tweet. Different from existing disaster-specific summarizers, we model tweet summarization as a supervised task. Such an approach can automatically learn summary-worthy features, and can therefore generalize well across domains. When trained on the PHEME dataset [29], not only do we outperform the strongest baselines for the auxiliary task of verification/rumour detection, we also achieve 21 - 35% gains in the verified ratio of summary tweets, and 16 - 20% gains in ROUGE1-F1 scores over the existing state-of-the-art solutions for the primary task of trustworthy summarization.
Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or first principles are onerous or infeasible. Moreover, these models are high-dimensional but spatially correlated. It is, however, observed that the dynamics of high-fidelity models often evolve in low-dimensional manifolds. Furthermore, it is also known that for sufficiently smooth vector fields defining the nonlinear dynamics, a quadratic model can describe it accurately in an appropriate coordinate system, conferring to the McCormick relaxation idea in nonconvex optimization. Here, we aim at finding a low-dimensional embedding of high-fidelity dynamical data, ensuring a simple quadratic model to explain its dynamics. To that aim, this work leverages deep learning to identify low-dimensional quadratic embeddings for high-fidelity dynamical systems. Precisely, we identify the embedding of data using an autoencoder to have the desired property of the embedding. We also embed a Runge-Kutta method to avoid the time-derivative computations, which is often a challenge. We illustrate the ability of the approach by a couple of examples, arising in describing flow dynamics and the oscillatory tubular reactor model.
Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is a necessary step to draw conclusions from these data, and it often becomes quite essential to construct dynamical models using these data. We discuss a methodology to learn differential equation(s) using noisy and sparsely sampled measurements. In our methodology, the main innovation can be seen in of integration of deep neural networks with a classical numerical integration method. Precisely, we aim at learning a neural network that implicitly represents the data and an additional neural network that models the vector fields of the dependent variables. We combine these two networks by enforcing the constraint that the data at the next time-steps can be given by following a numerical integration scheme such as the fourth-order Runge-Kutta scheme. The proposed framework to learn a model predicting the vector field is highly effective under noisy measurements. The approach can handle scenarios where dependent variables are not available at the same temporal grid. We demonstrate the effectiveness of the proposed method to learning models using data obtained from various differential equations. The proposed approach provides a promising methodology to learn dynamic models, where the first-principle understanding remains opaque.
Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e.g., optimizing a process. Experimental data availability notwithstanding has increased significantly, but interpretable and explainable models in science and engineering yet remain incomprehensible. In this work, we blend machine learning and dictionary-based learning with numerical analysis tools to discover governing differential equations from noisy and sparsely-sampled measurement data. We utilize the fact that given a dictionary containing huge candidate nonlinear functions, dynamical models can often be described by a few appropriately chosen candidates. As a result, we obtain interpretable and parsimonious models which are prone to generalize better beyond the sampling regime. Additionally, we integrate a numerical integration framework with dictionary learning that yields differential equations without requiring or approximating derivative information at any stage. Hence, it is utterly effective in corrupted and sparsely-sampled data. We discuss its extension to governing equations, containing rational nonlinearities that typically appear in biological networks. Moreover, we generalized the method to governing equations that are subject to parameter variations and externally controlled inputs. We demonstrate the efficiency of the method to discover a number of diverse differential equations using noisy measurements, including a model describing neural dynamics, chaotic Lorenz model, Michaelis-Menten Kinetics, and a parameterized Hopf normal form.
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a dynamic model can be built, but for complex dynamic processes, appearing, e.g., in biology, chemical plants, neuroscience, financial markets, this often remains an onerous task. Hence, data-driven modeling of the dynamics process becomes an attractive choice and is supported by the rapid advancement in sensor and measurement technology. A data-driven approach, namely operator inference framework, models a dynamic process, where a particular structure of the nonlinear term is assumed. In this work, we suggest combining the operator inference with certain deep neural network approaches to infer the unknown nonlinear dynamics of the system. The approach uses recent advancements in deep learning and possible prior knowledge of the process if possible. We also briefly discuss several extensions and advantages of the proposed methodology. We demonstrate that the proposed methodology accomplishes the desired tasks for dynamics processes encountered in neural dynamics and the glycolytic oscillator.
Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic Mode Decomposition and Operator Inference. With this work, we suggest a new approach to learning structured low-order models for incompressible flow from data that can be used for engineering studies such as control, optimization, and simulation. To that end, we utilize the intrinsic structure of the Navier-Stokes equations for incompressible flows and show that learning dynamics of the velocity and pressure can be decoupled, thus leading to an efficient operator inference approach for learning the underlying dynamics of incompressible flows. Furthermore, we show the operator inference performance in learning low-order models using two benchmark problems and compare with an intrusive method, namely proper orthogonal decomposition, and other data-driven approaches.
Souradip Guha, Ankan Mullick, Jatin Agrawal et al.
The number of published articles in the field of materials science is growing rapidly every year. This comparatively unstructured data source, which contains a large amount of information, has a restriction on its re-usability, as the information needed to carry out further calculations using the data in it must be extracted manually. It is very important to obtain valid and contextually correct information from the online (offline) data, as it can be useful not only to generate inputs for further calculations, but also to incorporate them into a querying framework. Retaining this context as a priority, we have developed an automated tool, MatScIE (Material Scince Information Extractor) that can extract relevant information from material science literature and make a structured database that is much easier to use for material simulations. Specifically, we extract the material details, methods, code, parameters, and structure from the various research articles. Finally, we created a web application where users can upload published articles and view/download the information obtained from this tool and can create their own databases for their personal uses.
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not only of low-rank but they also exhibit sparsity in a transformed space. In this work, we propose a new problem formulation in such a way that we seek to recover an image that is of low-rank and has sparsity in a transformed domain. We further discuss various non-convex non-smooth surrogates of the rank function, leading to a relaxed problem. Then, we present an efficient iterative scheme to solve the relaxed problem that essentially employs the (weighted) singular value thresholding at each iteration. Furthermore, we discuss the convergence properties of the proposed iterative method. We perform extensive experiments, showing that the proposed algorithm outperforms state-of-the-art methodologies in recovering images.
This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated in the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion-reaction Chafee-Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.
In this work, we investigate a model order reduction scheme for polynomial parametric systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order system, interpolating the defined generalized transfer functions at a given set of interpolation points. Furthermore, we provide a method, inspired by the Loewner approach for linear and (quadratic-)bilinear systems, to determine a good-quality reduced-order system in an automatic way. We also discuss the computational issues related to the proposed method and a potential application of CUR matrix approximation in order to further speed-up simulations of reduced-order systems. We test the efficiency of the proposed methods via several numerical examples.
This paper presents AppTechMiner, a rule-based information extraction framework that automatically constructs a knowledge base of all application areas and problem solving techniques. Techniques include tools, methods, datasets or evaluation metrics. We also categorize individual research articles based on their application areas and the techniques proposed/improved in the article. Our system achieves high average precision (~82%) and recall (~84%) in knowledge base creation. It also performs well in application and technique assignment to an individual article (average accuracy ~66%). In the end, we further present two use cases presenting a trivial information retrieval system and an extensive temporal analysis of the usage of techniques and application areas. At present, we demonstrate the framework for the domain of computational linguistics but this can be easily generalized to any other field of research.
Abhik Jana, Sruthi Mooriyath, Animesh Mukherjee et al.
In order to disseminate the exponential extent of knowledge being produced in the form of scientific publications, it would be best to design mechanisms that connect it with already existing rich repository of concepts -- the Wikipedia. Not only does it make scientific reading simple and easy (by connecting the involved concepts used in the scientific articles to their Wikipedia explanations) but also improves the overall quality of the article. In this paper, we present a novel metapath based method, WikiM, to efficiently wikify scientific abstracts -- a topic that has been rarely investigated in the literature. One of the prime motivations for this work comes from the observation that, wikified abstracts of scientific documents help a reader to decide better, in comparison to the plain abstracts, whether (s)he would be interested to read the full article. We perform mention extraction mostly through traditional tf-idf measures coupled with a set of smart filters. The entity linking heavily leverages on the rich citation and author publication networks. Our observation is that various metapaths defined over these networks can significantly enhance the overall performance of the system. For mention extraction and entity linking, we outperform most of the competing state-of-the-art techniques by a large margin arriving at precision values of 72.42% and 73.8% respectively over a dataset from the ACL Anthology Network. In order to establish the robustness of our scheme, we wikify three other datasets and get precision values of 63.41%-94.03% and 67.67%-73.29% respectively for the mention extraction and the entity linking phase.
Every field of research consists of multiple application areas with various techniques routinely used to solve problems in these wide range of application areas. With the exponential growth in research volumes, it has become difficult to keep track of the ever-growing number of application areas as well as the corresponding problem solving techniques. In this paper, we consider the computational linguistics domain and present a novel information extraction system that automatically constructs a pool of all application areas in this domain and appropriately links them with corresponding problem solving techniques. Further, we categorize individual research articles based on their application area and the techniques proposed/used in the article. k-gram based discounting method along with handwritten rules and bootstrapped pattern learning is employed to extract application areas. Subsequently, a language modeling approach is proposed to characterize each article based on its application area. Similarly, regular expressions and high-scoring noun phrases are used for the extraction of the problem solving techniques. We propose a greedy approach to characterize each article based on the techniques. Towards the end, we present a table representing the most frequent techniques adopted for a particular application area. Finally, we propose three use cases presenting an extensive temporal analysis of the usage of techniques and application areas.