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One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…
We investigate the parameterization of deep neural networks that by design satisfy the continuity equation, a fundamental conservation law. This is enabled by the observation that any solution of the continuity equation can be represented…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Many engineering and scientific fields have recently become interested in modeling terms in partial differential equations (PDEs) with neural networks, which requires solving the inverse problem of learning neural network terms from…
We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).…
Federated learning (FL), aimed at leveraging vast distributed datasets, confronts a crucial challenge: the heterogeneity of data across different silos. While previous studies have explored discrete representations to enhance model…
Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…
Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…
Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining…
Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range…
This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. The proposed framework learns an operator from the…
Existing work in scientific machine learning (SciML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical partial differential equation (PDE) solvers. Of these, Neural…
Neural networks have been demonstrated to be able to accelerate the modeling and inverse design of optical and electromagnetic devices by serving as fast surrogates for electromagnetic solvers. Nevertheless, such neural networks can be…
Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…
As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…
Designing neural networks within a Hamiltonian framework offers a principled way to ensure that conservation laws are respected in physical systems. While promising, these capabilities have been largely limited to discrete, analytically…
Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…
Reinforcement learning in partially observed Markov decision processes (POMDPs) faces two challenges. (i) It often takes the full history to predict the future, which induces a sample complexity that scales exponentially with the horizon.…