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Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…

The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential…

Neural architecture search has attracted wide attentions in both academia and industry. To accelerate it, researchers proposed weight-sharing methods which first train a super-network to reuse computation among different operators, from…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations…

With the rapid improvement of machine learning (ML) models, cognitive scientists are increasingly asking about their alignment with how humans think. Here, we ask this question for computer vision models and human sensitivity to geometric…

We present a data-driven, space-time continuous framework to learn surrogate models for complex physical systems described by advection-dominated partial differential equations. Those systems have slow-decaying Kolmogorov n-width that…

AI-driven surrogate modeling has become an increasingly effective alternative to physics-based simulations for 3D design, analysis, and manufacturing. These models leverage data-driven methods to predict physical quantities traditionally…

Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

Many climate processes are characterized using large systems of nonlinear differential equations; this, along with the immense amount of data required to parameterize complex interactions, means that Earth-System Model (ESM) simulations may…

Machine learning surrogate emulators are needed in engineering design and optimization tasks to rapidly emulate computationally expensive physics-based models. In micromechanics problems the local full-field response variables are desired…

Neural architecture search (NAS) faces a challenge in balancing the exploration of expressive, broad search spaces that enable architectural innovation with the need for efficient evaluation of architectures to effectively search such…

We introduce Universal Solution Manifold Network (USM-Net), a novel surrogate model, based on Artificial Neural Networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. Our…

While classical forms of stochastic gradient descent algorithm treat the different coordinates in the same way, a framework allowing for adaptive (non uniform) coordinate sampling is developed to leverage structure in data. In a non-convex…

Invariant models, one important class of geometric deep learning models, are capable of generating meaningful geometric representations by leveraging informative geometric features in point clouds. These models are characterized by their…

Weight-sharing is one of the pillars behind Convolutional Neural Networks and their successes. However, in physical neural systems such as the brain, weight-sharing is implausible. This discrepancy raises the fundamental question of whether…

Surrogate models are used to reduce the burden of expensive-to-evaluate objective functions in optimization. By creating models which map genomes to objective values, these models can estimate the performance of unknown inputs, and so be…

Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…