Jeyan Thiyagalingam

Luisa Lucie-Smith, Hiranya V. Peiris, Andrew Pontzen et al.

The density profiles of dark matter halos are typically modeled using empirical formulae fitted to the density profiles of relaxed halo populations. We present a neural network model that is trained to learn the mapping from the raw density field containing each halo to the dark matter density profile. We show that the model recovers the widely-used Navarro-Frenk-White (NFW) profile out to the virial radius, and can additionally describe the variability in the outer profile of the halos. The neural network architecture consists of a supervised encoder-decoder framework, which first compresses the density inputs into a low-dimensional latent representation, and then outputs $ρ(r)$ for any desired value of radius $r$. The latent representation contains all the information used by the model to predict the density profiles. This allows us to interpret the latent representation by quantifying the mutual information between the representation and the halos' ground-truth density profiles. A two-dimensional representation is sufficient to accurately model the density profiles up to the virial radius; however, a three-dimensional representation is required to describe the outer profiles beyond the virial radius. The additional dimension in the representation contains information about the infalling material in the outer profiles of dark matter halos, thus discovering the splashback boundary of halos without prior knowledge of the halos' dynamical history.

Gregor von Laszewski, Wesley Brewer, Jeyan Thiyagalingam et al.

Benchmarks are a cornerstone of modern machine learning, enabling reproducibility, comparison, and scientific progress. However, AI benchmarks are increasingly complex, requiring dynamic, AI-focused workflows. Rapid evolution in model architectures, scale, datasets, and deployment contexts makes evaluation a moving target. Large language models often memorize static benchmarks, causing a gap between benchmark results and real-world performance. Beyond traditional static benchmarks, continuous adaptive benchmarking frameworks are needed to align scientific assessment with deployment risks. This calls for skills and education in AI Benchmark Carpentry. From our experience with MLCommons, educational initiatives, and programs like the DOE's Trillion Parameter Consortium, key barriers include high resource demands, limited access to specialized hardware, lack of benchmark design expertise, and uncertainty in relating results to application domains. Current benchmarks often emphasize peak performance on top-tier hardware, offering limited guidance for diverse, real-world scenarios. Benchmarking must become dynamic, incorporating evolving models, updated data, and heterogeneous platforms while maintaining transparency, reproducibility, and interpretability. Democratization requires both technical innovation and systematic education across levels, building sustained expertise in benchmark design and use. Benchmarks should support application-relevant comparisons, enabling informed, context-sensitive decisions. Dynamic, inclusive benchmarking will ensure evaluation keeps pace with AI evolution and supports responsible, reproducible, and accessible AI deployment. Community efforts can provide a foundation for AI Benchmark Carpentry.

Kuangdai Leng, Jeyan Thiyagalingam

We shed light on a pitfall and an opportunity in physics-informed neural networks (PINNs). We prove that a multilayer perceptron (MLP) only with ReLU (Rectified Linear Unit) or ReLU-like Lipschitz activation functions will always lead to a vanished Hessian. Such a network-imposed constraint contradicts any second- or higher-order partial differential equations (PDEs). Therefore, a ReLU-based MLP cannot form a permissible function space for the approximation of their solutions. Inspired by this pitfall, we prove that a linear PDE up to the $n$-th order can be strictly satisfied by an MLP with $C^n$ activation functions when the weights of its output layer lie on a certain hyperplane, as called the out-layer-hyperplane. An MLP equipped with the out-layer-hyperplane becomes "physics-enforced", no longer requiring a loss function for the PDE itself (but only those for the initial and boundary conditions). Such a hyperplane exists not only for MLPs but for any network architecture tailed by a fully-connected hidden layer. To our knowledge, this should be the first PINN architecture that enforces point-wise correctness of PDEs. We show a closed-form expression of the out-layer-hyperplane for second-order linear PDEs, which can be generalised to higher-order nonlinear PDEs.

Ali Zahir, Ashiq Anjum, Mark Wilkinson et al.

The growing complexity and scale of scientific workflows in high performance computing (HPC) environments have led to significant challenges in managing energy consumption without compromising computational performance. Traditional scheduling strategies often fail to account for the complex interplay between thermal dynamics, workload diversity, and system scalability, leading to inefficient and unsustainable energy usage. This paper introduces a novel, scalable, and AI-assisted scheduling framework for optimizing energy consumption in HPC environments without compromising performance. Central to our approach is the integration of Computational Fluid Dynamics (CFD) with a Physics-Informed Variational Autoencoder (PIVAE), enabling the generation of physically realistic synthetic workload data that bridges the gap between thermodynamic behavior and scheduler decision-making in complex, multi-scale HPC environments. By categorizing workflows based on resource utilization profiles, we evaluate multiple scheduling strategies such as Locality Aware and Speculative Aware Scheduling. These workflows, ranging from event reconstruction to anomaly detection, represent diverse computational intensities. Our results show that modest reductions in CPU performance (e.g., to 15%) can yield substantial energy savings (up to 10%) with only minor turnaround time increases (approximately 5-6%), identifying an optimal operational sweet spot. This work demonstrates how physics-informed generative modeling can enable adaptive, sustainable, and data-efficient scheduling for next-generation HPC infrastructures.

Emily Lu, Gabriel Perez, Peter Baker et al.

Unravelling the complex processes governing battery degradation is critical to the energy transition, yet the efficacy of operando characterisation is severely constrained by a lack of Reliability, Representativeness, and Reproducibility (the 3Rs). Current methods rely on bespoke hardware and passive, pre-programmed methodologies that are ill-equipped to capture stochastic failure events. Here, using the Rutherford Appleton Laboratory's multi-modal toolkit as a case study, we expose the systemic inability of conventional experiments to capture transient phenomena like dendrite initiation. To address this, we propose Heuristic Operando experiments: a framework where an AI pilot leverages physics-based digital twins to actively steer the beamline to predict and deterministically capture these rare events. Distinct from uncertainty-driven active learning, this proactive search anticipates failure precursors, redefining experimental efficiency via an entropy-based metric that prioritises scientific insight per photon, neutron, or muon. By focusing measurements only on mechanistically decisive moments, this framework simultaneously mitigates beam damage and drastically reduces data redundancy. When integrated with FAIR data principles, this approach serves as a blueprint for the trusted autonomous battery laboratories of the future.

Kuangdai Leng, Mallikarjun Shankar, Jeyan Thiyagalingam

Automatic differentiation (AD) is a critical step in physics-informed machine learning, required for computing the high-order derivatives of network output w.r.t. coordinates of collocation points. In this paper, we present a novel and lightweight algorithm to conduct AD for physics-informed operator learning, which we call the trick of Zero Coordinate Shift (ZCS). Instead of making all sampled coordinates as leaf variables, ZCS introduces only one scalar-valued leaf variable for each spatial or temporal dimension, simplifying the wanted derivatives from "many-roots-many-leaves" to "one-root-many-leaves" whereby reverse-mode AD becomes directly utilisable. It has led to an outstanding performance leap by avoiding the duplication of the computational graph along the dimension of functions (physical parameters). ZCS is easy to implement with current deep learning libraries; our own implementation is achieved by extending the DeepXDE package. We carry out a comprehensive benchmark analysis and several case studies, training physics-informed DeepONets to solve partial differential equations (PDEs) without data. The results show that ZCS has persistently reduced GPU memory consumption and wall time for training by an order of magnitude, and such reduction factor scales with the number of functions. As a low-level optimisation technique, ZCS imposes no restrictions on data, physics (PDE) or network architecture and does not compromise training results from any aspect.

Marjan Famili, Jola Mirecka, Camila Rangel Smith et al.

Learning compact and interpretable representations of data is a critical challenge in scientific image analysis. Here, we introduce Affinity-VAE, a generative model that enables us to impose our scientific intuition about the similarity of instances in the dataset on the learned representation during training. We demonstrate the utility of the approach in the scientific domain of cryo-electron tomography (cryo-ET) where a significant current challenge is to identify similar molecules within a noisy and low contrast tomographic image volume. This task is distinct from classification in that, at inference time, it is unknown whether an instance is part of the training set or not. We trained affinity-VAE using prior knowledge of protein structure to inform the latent space. Our model is able to create rotationally-invariant, morphologically homogeneous clusters in the latent representation, with improved cluster separation compared to other approaches. It achieves competitive performance on protein classification with the added benefit of disentangling object pose, structural similarity and an interpretable latent representation. In the context of cryo-ET data, affinity-VAE captures the orientation of identified proteins in 3D which can be used as a prior for subsequent scientific experiments. Extracting physical principles from a trained network is of significant importance in scientific imaging where a ground truth training set is not always feasible.

Kuangdai Leng, Jeyan Thiyagalingam

Convolution is a fundamental operation in image processing and machine learning. Aimed primarily at maintaining image size, padding is a key ingredient of convolution, which, however, can introduce undesirable boundary effects. We present a non-padding-based method for size-keeping convolution based on the preservation of differential characteristics of kernels. The main idea is to make convolution over an incomplete sliding window "collapse" to a linear differential operator evaluated locally at its central pixel, which no longer requires information from the neighbouring missing pixels. While the underlying theory is rigorous, our final formula turns out to be simple: the convolution over an incomplete window is achieved by convolving its nearest complete window with a transformed kernel. This formula is computationally lightweight, involving neither interpolation or extrapolation nor restrictions on image and kernel sizes. Our method favours data with smooth boundaries, such as high-resolution images and fields from physics. Our experiments include: i) filtering analytical and non-analytical fields from computational physics and, ii) training convolutional neural networks (CNNs) for the tasks of image classification, semantic segmentation and super-resolution reconstruction. In all these experiments, our method has exhibited visible superiority over the compared ones.

Kuangdai Leng, Jia Bi, Jaehoon Cha et al.

The Moving Sofa Problem, formally proposed by Leo Moser in 1966, seeks to determine the largest area of a two-dimensional shape that can navigate through an $L$-shaped corridor with unit width. The current best lower bound is about 2.2195, achieved by Joseph Gerver in 1992, though its global optimality remains unproven. In this paper, we investigate this problem by leveraging the universal approximation strength and computational efficiency of neural networks. We report two approaches, both supporting Gerver's conjecture that his shape is the unique global maximum. Our first approach is continuous function learning. We drop Gerver's assumptions that i) the rotation of the corridor is monotonic and symmetric and, ii) the trajectory of its corner as a function of rotation is continuously differentiable. We parameterize rotation and trajectory by independent piecewise linear neural networks (with input being some pseudo time), allowing for rich movements such as backward rotation and pure translation. We then compute the sofa area as a differentiable function of rotation and trajectory using our "waterfall" algorithm. Our final loss function includes differential terms and initial conditions, leveraging the principles of physics-informed machine learning. Under such settings, extensive training starting from diverse function initialization and hyperparameters is conducted, unexceptionally showing rapid convergence to Gerver's solution. Our second approach is via discrete optimization of the Kallus-Romik upper bound, which converges to the maximum sofa area from above as the number of rotation angles increases. We uplift this number to 10000 to reveal its asymptotic behavior. It turns out that the upper bound yielded by our models does converge to Gerver's area (within an error of 0.01% when the number of angles reaches 2100). We also improve their five-angle upper bound from 2.37 to 2.3337.

Saiful Khan, Scott Jones, Benjamin Bach et al.

We present a method to create storytelling visualization with time series data. Many personal decisions nowadays rely on access to dynamic data regularly, as we have seen during the COVID-19 pandemic. It is thus desirable to construct storytelling visualization for dynamic data that is selected by an individual for a specific context. Because of the need to tell data-dependent stories, predefined storyboards based on known data cannot accommodate dynamic data easily nor scale up to many different individuals and contexts. Motivated initially by the need to communicate time series data during the COVID-19 pandemic, we developed a novel computer-assisted method for meta-authoring of stories, which enables the design of storyboards that include feature-action patterns in anticipation of potential features that may appear in dynamically arrived or selected data. In addition to meta-storyboards involving COVID-19 data, we also present storyboards for telling stories about progress in a machine learning workflow. Our approach is complementary to traditional methods for authoring storytelling visualization, and provides an efficient means to construct data-dependent storyboards for different data-streams of similar contexts.

Varshitha Chennamsetti, Gregor von Laszewski, Ruochen Gu et al.

In this paper, we report on work performed for the MLCommons Science Working Group on the cloud masking benchmark. MLCommons is a consortium that develops and maintains several scientific benchmarks that aim to benefit developments in AI. The benchmarks are conducted on the High Performance Computing (HPC) Clusters of New York University and University of Virginia, as well as a commodity desktop. We provide a description of the cloud masking benchmark, as well as a summary of our submission to MLCommons on the benchmark experiment we conducted. It includes a modification to the reference implementation of the cloud masking benchmark enabling early stopping. This benchmark is executed on the NYU HPC through a custom batch script that runs the various experiments through the batch queuing system while allowing for variation on the number of epochs trained. Our submission includes the modified code, a custom batch script to modify epochs, documentation, and the benchmark results. We report the highest accuracy (scientific metric) and the average time taken (performance metric) for training and inference that was achieved on NYU HPC Greene. We also provide a comparison of the compute capabilities between different systems by running the benchmark for one epoch. Our submission can be found in a Globus repository that is accessible to MLCommons Science Working Group.

Jaehoon Cha, Jeyan Thiyagalingam

Noting the importance of factorizing (or disentangling) the latent space, we propose a novel, non-probabilistic disentangling framework for autoencoders, based on the principles of symmetry transformations in group-theory. To the best of our knowledge, this is the first deterministic model that is aiming to achieve disentanglement based on autoencoders without regularizers. The proposed model is compared to seven state-of-the-art generative models based on autoencoders and evaluated based on five supervised disentanglement metrics. The experimental results show that the proposed model can have better disentanglement when variances of each features are different. We believe that this model leads to a new field for disentanglement learning based on autoencoders without regularizers.

Jeyan Thiyagalingam, Mallikarjun Shankar, Geoffrey Fox et al.

The breakthrough in Deep Learning neural networks has transformed the use of AI and machine learning technologies for the analysis of very large experimental datasets. These datasets are typically generated by large-scale experimental facilities at national laboratories. In the context of science, scientific machine learning focuses on training machines to identify patterns, trends, and anomalies to extract meaningful scientific insights from such datasets. With a new generation of experimental facilities, the rate of data generation and the scale of data volumes will increasingly require the use of more automated data analysis. At present, identifying the most appropriate machine learning algorithm for the analysis of any given scientific dataset is still a challenge for scientists. This is due to many different machine learning frameworks, computer architectures, and machine learning models. Historically, for modelling and simulation on HPC systems such problems have been addressed through benchmarking computer applications, algorithms, and architectures. Extending such a benchmarking approach and identifying metrics for the application of machine learning methods to scientific datasets is a new challenge for both scientists and computer scientists. In this paper, we describe our approach to the development of scientific machine learning benchmarks and review other approaches to benchmarking scientific machine learning.

Luisa Lucie-Smith, Hiranya V. Peiris, Andrew Pontzen et al.

The evolution of linear initial conditions present in the early universe into extended halos of dark matter at late times can be computed using cosmological simulations. However, a theoretical understanding of this complex process remains elusive; in particular, the role of anisotropic information in the initial conditions in establishing the final mass of dark matter halos remains a long-standing puzzle. Here, we build a deep learning framework to investigate this question. We train a three-dimensional convolutional neural network (CNN) to predict the mass of dark matter halos from the initial conditions, and quantify in full generality the amounts of information in the isotropic and anisotropic aspects of the initial density field about final halo masses. We find that anisotropies add a small, albeit statistically significant amount of information over that contained within spherical averages of the density field about final halo mass. However, the overall scatter in the final mass predictions does not change qualitatively with this additional information, only decreasing from 0.9 dex to 0.7 dex. Given such a small improvement, our results demonstrate that isotropic aspects of the initial density field essentially saturate the relevant information about final halo mass. Therefore, instead of searching for information directly encoded in initial conditions anisotropies, a more promising route to accurate, fast halo mass predictions is to add approximate dynamical information based e.g. on perturbation theory. More broadly, our results indicate that deep learning frameworks can provide a powerful tool for extracting physical insight into cosmological structure formation.