Amit Chakraborty

Yaofeng Desmond Zhong, Tongtao Zhang, Amit Chakraborty et al.

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections to avoid the problem of vanishing gradients, they can be viewed as the numerical integration of a differential equation. In this extended abstract, we build upon this connection and propose a modification of the internal architecture of a transformer layer. The proposed model places the multi-head attention sublayer and the MLP sublayer parallel to each other. Our experiments show that this simple modification improves the performance of transformer networks in multiple tasks. Moreover, for the image classification task, we show that using neural ODE solvers with a sophisticated integration scheme further improves performance.

Shinjan Ghosh, Amit Chakraborty, Georgia Olympia Brikis et al.

Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the loss function to enhance generalization performance. Since simulating dynamics controlled by partial differential equations (PDEs) can be computationally expensive, PINNs have gained popularity in learning parametric surrogates for fluid flow problems governed by Navier-Stokes equations. In this work, we introduce RANS-PINN, a modified PINN framework, to predict flow fields (i.e., velocity and pressure) in high Reynolds number turbulent flow regimes. To account for the additional complexity introduced by turbulence, RANS-PINN employs a 2-equation eddy viscosity model based on a Reynolds-averaged Navier-Stokes (RANS) formulation. Furthermore, we adopt a novel training approach that ensures effective initialization and balance among the various components of the loss function. The effectiveness of the RANS-PINN framework is then demonstrated using a parametric PINN.

Tongtao Zhang, Biswadip Dey, Krishna Veeraraghavan et al.

Computational fluid dynamics (CFD) simulations, a critical tool in various engineering applications, often require significant time and compute power to predict flow properties. The high computational cost associated with CFD simulations significantly restricts the scope of design space exploration and limits their use in planning and operational control. To address this issue, machine learning (ML) based surrogate models have been proposed as a computationally efficient tool to accelerate CFD simulations. However, a lack of clarity about CFD data requirements often challenges the widespread adoption of ML-based surrogates among design engineers and CFD practitioners. In this work, we propose an ML-based surrogate model to predict the temperature distribution inside the cabin of a passenger vehicle under various operating conditions and use it to demonstrate the trade-off between prediction performance and training dataset size. Our results show that the prediction accuracy is high and stable even when the training size is gradually reduced from 2000 to 200. The ML-based surrogates also reduce the compute time from ~30 minutes to around ~9 milliseconds. Moreover, even when only 50 CFD simulations are used for training, the temperature trend (e.g., locations of hot/cold regions) predicted by the ML-surrogate matches quite well with the results from CFD simulations.

Valentin Duruisseaux, Amit Chakraborty

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain using traditional methods due to limited computational resources. A recent direction to circumvent these computational limitations is to use machine learning techniques for super-resolution, to reconstruct high-resolution numerical solutions from low-resolution simulations which can be obtained more efficiently. The proposed approach, the Super Resolution Operator Network (SROpNet), frames super-resolution as an operator learning problem and draws inspiration from existing architectures to learn continuous representations of solutions to parametric differential equations from low-resolution approximations, which can then be evaluated at any desired location. In addition, no restrictions are imposed on the locations of (the fixed number of) spatiotemporal sensors at which the low-resolution approximations are provided, thereby enabling the consideration of a broader spectrum of problems arising in practice, for which many existing super-resolution approaches are not well-suited.

Mohammed Aman Bhuiyan, Md Sazzad Hossain Adib, Samiul Basir Bhuiyan et al.

Automatic Speech Recognition (ASR) and speaker diarization in Bangla remain challenging due to long form recordings, diverse acoustic conditions, and significant speaker variability. This work addresses these two core tasks in Bangla spoken language understanding by developing robust systems for long form ASR and speaker diarization. For ASR (Problem 1), we fine tune the tugstugi bengaliai regional asr whisper medium model on a custom-curated dataset of approximately 15,000 chunked and aligned Bangla audio segments, employing full weight training with extensive data augmentation including noise injection, reverb simulation, echo, clipping distortion, and pitch/time perturbation. For speaker diarization (Problem 2), we fine-tune the pyannote/segmentation-3.0 model using PyTorch Lightning on the competition annotated diarization dataset, swapping the fine-tuned segmentation backbone into the pyannote/speaker-diarization-community-1 pipeline while retaining the pretrained speaker embedding and clustering components. Our ASR system achieves a Word Error Rate (WER) of 0.2441, while our diarization system achieves a Diarization Error Rate (DER) of 0.2392, both evaluated on the test set, demonstrating notable improvements over the respective pretrained baselines. We describe our complete pipeline, including data preprocessing, text normalization, audio augmentation, training strategies, inference optimization, and post-processing for both tasks.

Shinjan Ghosh, Amit Chakraborty, Georgia Olympia Brikis et al.

Computational fluid dynamics (CFD) solvers employing two-equation eddy viscosity models are the industry standard for simulating turbulent flows using the Reynolds-averaged Navier-Stokes (RANS) formulation. While these methods are computationally less expensive than direct numerical simulations, they can still incur significant computational costs to achieve the desired accuracy. In this context, physics-informed neural networks (PINNs) offer a promising approach for developing parametric surrogate models that leverage both existing, but limited CFD solutions and the governing differential equations to predict simulation outcomes in a computationally efficient, differentiable, and near real-time manner. In this work, we build upon the previously proposed RANS-PINN framework, which only focused on predicting flow over a cylinder. To investigate the efficacy of RANS-PINN as a viable approach to building parametric surrogate models, we investigate its accuracy in predicting relevant turbulent flow variables for both internal and external flows. To ensure training convergence with a more complex loss function, we adopt a novel sampling approach that exploits the domain geometry to ensure a proper balance among the contributions from various regions within the solution domain. The effectiveness of this framework is then demonstrated for two scenarios that represent a broad class of internal and external flow problems.

Rajat Arora, Pratik Kakkar, Biswadip Dey et al.

This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during training, the proposed framework uses a simple strategy with no added computational complexity for selecting scalar weights that balance the interplay between different terms in the physics-based loss function. In addition, we highlight a fundamental challenge involving the selection of appropriate model outputs so that the mechanical problem can be faithfully solved using a PINN-based approach. We demonstrate the effectiveness of this approach by studying two test problems modeling the elastic-viscoplastic deformation in solids at different strain rates and temperatures, respectively. Our results show that the proposed PINN-based approach can accurately predict the spatio-temporal evolution of deformation in elastic-viscoplastic materials.

Haoran Su, Yaofeng Desmond Zhong, Biswadip Dey et al.

Emergency vehicles (EMVs) play a critical role in a city's response to time-critical events such as medical emergencies and fire outbreaks. The existing approaches to reduce EMV travel time employ route optimization and traffic signal pre-emption without accounting for the coupling between route these two subproblems. As a result, the planned route often becomes suboptimal. In addition, these approaches also do not focus on minimizing disruption to the overall traffic flow. To address these issues, we introduce EMVLight in this paper. This is a decentralized reinforcement learning (RL) framework for simultaneous dynamic routing and traffic signal control. EMVLight extends Dijkstra's algorithm to efficiently update the optimal route for an EMV in real-time as it travels through the traffic network. Consequently, the decentralized RL agents learn network-level cooperative traffic signal phase strategies that reduce EMV travel time and the average travel time of non-EMVs in the network. We have carried out comprehensive experiments with synthetic and real-world maps to demonstrate this benefit. Our results show that EMVLight outperforms benchmark transportation engineering techniques as well as existing RL-based traffic signal control methods.

Haoran Su, Yaofeng Desmond Zhong, Biswadip Dey et al.

Emergency vehicles (EMVs) play a crucial role in responding to time-critical events such as medical emergencies and fire outbreaks in an urban area. The less time EMVs spend traveling through the traffic, the more likely it would help save people's lives and reduce property loss. To reduce the travel time of EMVs, prior work has used route optimization based on historical traffic-flow data and traffic signal pre-emption based on the optimal route. However, traffic signal pre-emption dynamically changes the traffic flow which, in turn, modifies the optimal route of an EMV. In addition, traffic signal pre-emption practices usually lead to significant disturbances in traffic flow and subsequently increase the travel time for non-EMVs. In this paper, we propose EMVLight, a decentralized reinforcement learning (RL) framework for simultaneous dynamic routing and traffic signal control. EMVLight extends Dijkstra's algorithm to efficiently update the optimal route for the EMVs in real time as it travels through the traffic network. The decentralized RL agents learn network-level cooperative traffic signal phase strategies that not only reduce EMV travel time but also reduce the average travel time of non-EMVs in the network. This benefit has been demonstrated through comprehensive experiments with synthetic and real-world maps. These experiments show that EMVLight outperforms benchmark transportation engineering techniques and existing RL-based signal control methods.

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty

The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or Hamiltonian dynamics into the neural network architecture. These existing approaches are based on differential equations, which do not allow discontinuity in the states and thereby limit the class of systems one can learn. However, in reality, most physical systems, such as legged robots and robotic manipulators, involve contacts and collisions, which introduce discontinuities in the states. In this paper, we introduce a differentiable contact model, which can capture contact mechanics: frictionless/frictional, as well as elastic/inelastic. This model can also accommodate inequality constraints, such as limits on the joint angles. The proposed contact model extends the scope of Lagrangian and Hamiltonian neural networks by allowing simultaneous learning of contact and system properties. We demonstrate this framework on a series of challenging 2D and 3D physical systems with different coefficients of restitution and friction. The learned dynamics can be used as a differentiable physics simulator for downstream gradient-based optimization tasks, such as planning and control.

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty

The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while using neural networks for learning dynamics from observed time-series data. In this work, we survey ten recently proposed energy-conserving neural network models, including HNN, LNN, DeLaN, SymODEN, CHNN, CLNN and their variants. We provide a compact derivation of the theory behind these models and explain their similarities and differences. Their performance are compared in 4 physical systems. We point out the possibility of leveraging some of these energy-conserving models to design energy-based controllers.

Udari Madhushani, Biswadip Dey, Naomi Ehrich Leonard et al.

Value function based reinforcement learning (RL) algorithms, for example, $Q$-learning, learn optimal policies from datasets of actions, rewards, and state transitions. However, when the underlying state transition dynamics are stochastic and evolve on a high-dimensional space, generating independent and identically distributed (IID) data samples for creating these datasets poses a significant challenge due to the intractability of the associated normalizing integral. In these scenarios, Hamiltonian Monte Carlo (HMC) sampling offers a computationally tractable way to generate data for training RL algorithms. In this paper, we introduce a framework, called \textit{Hamiltonian $Q$-Learning}, that demonstrates, both theoretically and empirically, that $Q$ values can be learned from a dataset generated by HMC samples of actions, rewards, and state transitions. Furthermore, to exploit the underlying low-rank structure of the $Q$ function, Hamiltonian $Q$-Learning uses a matrix completion algorithm for reconstructing the updated $Q$ function from $Q$ value updates over a much smaller subset of state-action pairs. Thus, by providing an efficient way to apply $Q$-learning in stochastic, high-dimensional settings, the proposed approach broadens the scope of RL algorithms for real-world applications.

Tongtao Zhang, Biswadip Dey, Pratik Kakkar et al.

Incompressible fluid flow around a cylinder is one of the classical problems in fluid-dynamics with strong relevance with many real-world engineering problems, for example, design of offshore structures or design of a pin-fin heat exchanger. Thus learning a high-accuracy surrogate for this problem can demonstrate the efficacy of a novel machine learning approach. In this work, we propose a physics-informed neural network (PINN) architecture for learning the relationship between simulation output and the underlying geometry and boundary conditions. In addition to using a physics-based regularization term, the proposed approach also exploits the underlying physics to learn a set of Fourier features, i.e. frequency and phase offset parameters, and then use them for predicting flow velocity and pressure over the spatio-temporal domain. We demonstrate this approach by predicting simulation results over out of range time interval and for novel design conditions. Our results show that incorporation of Fourier features improves the generalization performance over both temporal domain and design space.

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty

In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size, Dissipative SymODEN encodes the port-Hamiltonian dynamics with energy dissipation and external input into the design of its computation graph and learns the dynamics in a structured way. The learned model, by revealing key aspects of the system, such as the inertia, dissipation, and potential energy, paves the way for energy-based controllers.

Akshay Iyer, Biswadip Dey, Arindam Dasgupta et al.

Microstructures of a material form the bridge linking processing conditions - which can be controlled, to the material property - which is the primary interest in engineering applications. Thus a critical task in material design is establishing the processing-structure relationship, which requires domain expertise and techniques that can model the high-dimensional material microstructure. This work proposes a deep learning based approach that models the processing-structure relationship as a conditional image synthesis problem. In particular, we develop an auxiliary classifier Wasserstein GAN with gradient penalty (ACWGAN-GP) to synthesize microstructures under a given processing condition. This approach is free of feature engineering, requires modest domain knowledge and is applicable to a wide range of material systems. We demonstrate this approach using the ultra high carbon steel (UHCS) database, where each microstructure is annotated with a label describing the cooling method it was subjected to. Our results show that ACWGAN-GP can synthesize high-quality multiphase microstructures for a given cooling method.

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty

In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate inductive bias by designing the associated computation graph in a physics-informed manner. In particular, we enforce Hamiltonian dynamics with control to learn the underlying dynamics in a transparent way, which can then be leveraged to draw insight about relevant physical aspects of the system, such as mass and potential energy. In addition, we propose a parametrization which can enforce this Hamiltonian formalism even when the generalized coordinate data is embedded in a high-dimensional space or we can only access velocity data instead of generalized momentum. This framework, by offering interpretable, physically-consistent models for physical systems, opens up new possibilities for synthesizing model-based control strategies.

Amit Chakraborty, Sung Hak Lim, Mihoko M. Nojiri

Classification of jets with deep learning has gained significant attention in recent times. However, the performance of deep neural networks is often achieved at the cost of interpretability. Here we propose an interpretable network trained on the jet spectrum $S_{2}(R)$ which is a two-point correlation function of the jet constituents. The spectrum can be derived from a functional Taylor series of an arbitrary jet classifier function of energy flows. An interpretable network can be obtained by truncating the series. The intermediate feature of the network is an infrared and collinear safe C-correlator which allows us to estimate the importance of a $S_{2}(R)$ deposit at an angular scale R in the classification. The performance of the architecture is comparable to that of a convolutional neural network (CNN) trained on jet images, although the number of inputs and complexity of architecture is significantly simpler than the CNN classifier. We consider two examples: one is the classification of two-prong jets which differ in color charge of the mother particle, and the other is a comparison between Pythia 8 and Herwig 7 generated jets.

Kai Fan, Qi Wei, Wenlin Wang et al.

We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy widely used in regularized iterative algorithm to tackle inverse problems, the mapping is decomposed into two networks, with one handling the inversion of the physical forward model associated with the data term and one handling the denoising of the output from the former network, i.e., the inverted version, associated with the prior/regularization term. The two networks are trained jointly to learn the end-to-end mapping, getting rid of a two-step training. The training is annealing as the intermediate variable between these two networks bridges the gap between the input (the degraded version of output) and output and progressively approaches to the ground-truth. The proposed network, referred to as InverseNet, is flexible in the sense that most of the existing end-to-end network structure can be leveraged in the first network and most of the existing denoising network structure can be used in the second one. Extensive experiments on both synthetic data and real datasets on the tasks, motion deblurring, super-resolution, and colorization, demonstrate the efficiency and accuracy of the proposed method compared with other image processing algorithms.

Feipeng Zhao, Martin Renqiang Min, Chen Shen et al.

Previous models for learning entity and relationship embeddings of knowledge graphs such as TransE, TransH, and TransR aim to explore new links based on learned representations. However, these models interpret relationships as simple translations on entity embeddings. In this paper, we try to learn more complex connections between entities and relationships. In particular, we use a Convolutional Neural Network (CNN) to learn entity and relationship representations in knowledge graphs. In our model, we treat entities and relationships as one-dimensional numerical sequences with the same length. After that, we combine each triplet of head, relationship, and tail together as a matrix with height 3. CNN is applied to the triplets to get confidence scores. Positive and manually corrupted negative triplets are used to train the embeddings and the CNN model simultaneously. Experimental results on public benchmark datasets show that the proposed model outperforms state-of-the-art models on exploring unseen relationships, which proves that CNN is effective to learn complex interactive patterns between entities and relationships.

Yangyang Xu, Ioannis Akrotirianakis, Amit Chakraborty

The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with $\ell_1$-regularization. This paper considers the Huberized SVM (HSVM), which uses a differentiable approximation of the hinge loss function. We first explore the use of the Proximal Gradient (PG) method to solving binary-class HSVM (B-HSVM) and then generalize it to multi-class HSVM (M-HSVM). Under strong convexity assumptions, we show that our algorithm converges linearly. In addition, we give a finite convergence result about the support of the solution, based on which we further accelerate the algorithm by a two-stage method. We present extensive numerical experiments on both synthetic and real datasets which demonstrate the superiority of our methods over some state-of-the-art methods for both binary- and multi-class SVMs.

Yangyang Xu, Ioannis Akrotirianakis, Amit Chakraborty

The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by considering their dual formulations which are quadratic programs and can be solved by standard second-order methods. However, the duals of MSVMs with regularizers are usually more difficult to formulate and computationally very expensive to solve. This paper focuses on several regularized MSVMs and extends the alternating direction method of multiplier (ADMM) to these MSVMs. Using a splitting technique, all considered MSVMs are written as two-block convex programs, for which the ADMM has global convergence guarantees. Numerical experiments on synthetic and real data demonstrate the high efficiency and accuracy of our algorithms.

Zhiwei Qin, Xiaocheng Tang, Ioannis Akrotirianakis et al.

We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipliers in the first phase, followed by an interior-point method for the classical SVM in the second phase. Both SVM formulations are adapted to knowledge incorporation. Our proposed algorithm addresses the challenges of automatic feature selection, high optimization accuracy, and algorithmic flexibility for taking advantage of prior knowledge. We demonstrate the effectiveness and efficiency of our algorithm and compare it with existing methods on a collection of synthetic and real-world data.