Joseph Bakarji

Philippe Martin Wyder, Judah Goldfeder, Alexey Yermakov et al.

Machine learning (ML) is transforming modeling and control in the physical, engineering, and biological sciences. However, rapid development has outpaced the creation of standardized, objective benchmarks - leading to weak baselines, reporting bias, and inconsistent evaluations across methods. This undermines reproducibility, misguides resource allocation, and obscures scientific progress. To address this, we propose a Common Task Framework (CTF) for scientific machine learning. The CTF features a curated set of datasets and task-specific metrics spanning forecasting, state reconstruction, and generalization under realistic constraints, including noise and limited data. Inspired by the success of CTFs in fields like natural language processing and computer vision, our framework provides a structured, rigorous foundation for head-to-head evaluation of diverse algorithms. As a first step, we benchmark methods on two canonical nonlinear systems: Kuramoto-Sivashinsky and Lorenz. These results illustrate the utility of the CTF in revealing method strengths, limitations, and suitability for specific classes of problems and diverse objectives. Next, we are launching a competition around a global real world sea surface temperature dataset with a true holdout dataset to foster community engagement. Our long-term vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets that raise the bar for rigor and reproducibility in scientific ML.

Stefano Riva, Carolina Introini, Antonio Cammi et al.

The demand for clean energy is ever increasing, with new nuclear technologies presenting a complementary solution to renewable energies. However, designing and operating these systems is exceptionally difficult, given the complexity of the physical phenomena that interact to form the system dynamics. While high-fidelity simulations help to understand the non-linear, multi-physics interactions within a reactor, they are computationally expensive and rarely suitable for real-time applications. Furthermore, model-based approaches are inherently sensitive to simplifying assumptions required to derive their governing equations and parameters, leading to inevitable discrepancies with real-world measurements. In contrast, Machine Learning (ML) methods have the potential to generate reliable surrogate models which may be able to quickly predict the system's behaviour. However, the number of data-driven methods that can potentially be used for this task is large and diverse. In a safety-critical setting such as nuclear engineering, a fair comparison of different ML methods, and a clear understanding of their advantages and limitations, is of paramount importance. To address this, we introduce a Common Task Framework (CTF) for ML in nuclear engineering, building upon previous efforts in dynamical systems and seismology. This CTF considers a curated set of datasets from different nuclear and nuclear-adjacent systems. The CTF evaluates the performance of a method on 12 established metrics, alongside a new paradigm focused on system monitoring from sparse measurements only. We illustrate the framework by benchmarking standard ML baselines against these datasets, revealing current method limitations. Our vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets, raising the bar for rigour and reproducibility in scientific ML for the nuclear industry.

Alexey Yermakov, Yue Zhao, Marine Denolle et al.

Seismology faces fundamental challenges in state forecasting and reconstruction (e.g., earthquake early warning and ground motion prediction) and managing the parametric variability of source locations, mechanisms, and Earth models (e.g., subsurface structure and topography effects). Addressing these with simulations is hindered by their massive scale, both in synthetic data volumes and numerical complexity, while real-data efforts are constrained by models that inadequately reflect the Earth's complexity and by sparse sensor measurements from the field. Recent machine learning (ML) efforts offer promise, but progress is obscured by a lack of proper characterization, fair reporting, and rigorous comparisons. To address this, we introduce a Common Task Framework (CTF) for ML for seismic wavefields, starting with three distinct wavefield datasets. Our CTF features a curated set of datasets at various scales (global, crustal, and local) and task-specific metrics spanning forecasting, reconstruction, and generalization under realistic constraints such as noise and limited data. Inspired by CTFs in fields like natural language processing, this framework provides a structured and rigorous foundation for head-to-head algorithm evaluation. We illustrate the evaluation procedure with scores reported for two of the datasets, showcasing the performance of various methods and foundation models for reconstructing seismic wavefields from both simulated and real-world sensor measurements. The CTF scores reveal the strengths, limitations, and suitability for specific problem classes. Our vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets, raising the bar for rigor and reproducibility in scientific ML.

Thomas Haschka, Joseph Bakarji

Recent advances in large language models enable documents to be represented as dense semantic embeddings, supporting similarity-based operations over large text collections. However, many web-scale systems still rely on flat clustering or predefined taxonomies, limiting insight into hierarchical topic relationships. In this paper we operationalize hierarchical density modeling on large language model embeddings in a way not previously explored. Instead of enforcing a fixed taxonomy or single clustering resolution, the method progressively relaxes local density constraints, revealing how compact semantic groups merge into broader thematic regions. The resulting tree encodes multi-scale semantic organization directly from data, making structural relationships between topics explicit. We evaluate the hierarchies on standard text benchmarks, showing that semantic alignment peaks at intermediate density levels and that abrupt transitions correspond to meaningful changes in semantic resolution. Beyond benchmarks, the approach is applied to large institutional and scientific corpora, exposing dominant fields, cross-disciplinary proximities, and emerging thematic clusters. By framing hierarchical structure as an emergent property of density in embedding spaces, this method provides an interpretable, multi-scale representation of semantic structure suitable for large, evolving text collections.

Andrei A. Klishin, Joseph Bakarji, J. Nathan Kutz et al.

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and parsimony via hyperparameter tuning. In this framework, statistical mechanics offers tools to analyze the interplay between complexity and fitness similarly to that of entropy and energy in physical systems. To establish this analogy, we define the hyperparameter optimization procedure as a two-level Bayesian inference problem that separates variable selection from coefficient inference and enables the computation of the posterior parameter distribution in closed form. Our approach provides uncertainty quantification, crucial in the low-data limit that is frequently encountered in real-world applications. A key advantage of employing statistical mechanical concepts, such as free energy and the partition function, is to connect the large data limit to thermodynamic limit and characterize the sparsity- and noise-induced phase transitions that delineate correct from incorrect identification. We thus provide a method for closed-loop inference, estimating the noise in a given model and checking if the model is tolerant to that noise amount. This perspective of sparse equation discovery is versatile and can be adapted to various other equation discovery algorithms.

Joseph Bakarji, Jared Callaham, Steven L. Brunton et al.

In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure for finding a set of dimensionless groups that spans the solution space, although this set is not unique. We propose an automated approach using the symmetric and self-similar structure of available measurement data to discover the dimensionless groups that best collapse this data to a lower dimensional space according to an optimal fit. We develop three data-driven techniques that use the Buckingham Pi theorem as a constraint: (i) a constrained optimization problem with a non-parametric input-output fitting function, (ii) a deep learning algorithm (BuckiNet) that projects the input parameter space to a lower dimension in the first layer, and (iii) a technique based on sparse identification of nonlinear dynamics (SINDy) to discover dimensionless equations whose coefficients parameterize the dynamics. We explore the accuracy, robustness and computational complexity of these methods as applied to three example problems: a bead on a rotating hoop, a laminar boundary layer, and Rayleigh-Bénard convection.

Joseph Bakarji, Kathleen Champion, J. Nathan Kutz et al.

A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens' theorem provides conditions for when it is possible to augment these partial measurements with time delayed information, resulting in an attractor that is diffeomorphic to that of the original full-state system. However, the coordinate transformation back to the original attractor is typically unknown, and learning the dynamics in the embedding space has remained an open challenge for decades. Here, we design a custom deep autoencoder network to learn a coordinate transformation from the delay embedded space into a new space where it is possible to represent the dynamics in a sparse, closed form. We demonstrate this approach on the Lorenz, Rössler, and Lotka-Volterra systems, learning dynamics from a single measurement variable. As a challenging example, we learn a Lorenz analogue from a single scalar variable extracted from a video of a chaotic waterwheel experiment. The resulting modeling framework combines deep learning to uncover effective coordinates and the sparse identification of nonlinear dynamics (SINDy) for interpretable modeling. Thus, we show that it is possible to simultaneously learn a closed-form model and the associated coordinate system for partially observed dynamics.

Joseph Bakarji, Daniel M. Tartakovsky

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning on simulated data can lead to such discovery. In both, the data are generated with a reliable but impractical model, e.g., molecular dynamics simulations, while a model on the scale of interest is uncertain, requiring phenomenological constitutive relations and ad-hoc approximations. We replace the human discovery of such models, which typically involves spatial/stochastic averaging or coarse-graining, with a machine-learning strategy based on sparse regression that can be executed in two modes. The first, direct equation-learning, discovers a differential operator from the whole dictionary. The second, constrained equation-learning, discovers only those terms in the differential operator that need to be discovered, i.e., learns closure approximations. We illustrate our approach by learning a deterministic equation that governs the spatiotemporal evolution of the probability density function of a system state whose dynamics are described by a nonlinear partial differential equation with random inputs. A series of examples demonstrates the accuracy, robustness, and limitations of our approach to equation discovery.

Joseph Bakarji

A music glove instrument equipped with force sensitive, flex and IMU sensors is trained on an electric piano to learn note sequences based on a time series of sensor inputs. Once trained, the glove is used on any surface to generate the sequence of notes most closely related to the hand motion. The data is collected manually by a performer wearing the glove and playing on an electric keyboard. The feature space is designed to account for the key hand motion, such as the thumb-under movement. Logistic regression along with bayesian belief networks are used learn the transition probabilities from one note to another. This work demonstrates a data-driven approach for digital musical instruments in general.