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This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…

The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel…

Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors…

In this paper, we advocate CPN-FedSL, a novel and flexible Federated Split Learning (FedSL) framework over Computing Power Network (CPN). We build a dedicated model to capture the basic settings and learning characteristics (e.g., training…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

A class of nonstandard pseudospectral time domain (PSTD) schemes for solving time-dependent hyperbolic and parabolic partial differential equations (PDEs) is introduced. These schemes use the Fourier collocation spectral method to compute…

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…

Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…

A novel solve-training framework is proposed to train neural network in representing low dimensional solution maps of physical models. Solve-training framework uses the neural network as the ansatz of the solution map and train the network…

Decentralized machine learning (DML) supports collaborative training in large-scale networks with no central server. It is sensitive to the quality and reliability of inter-device communications that result in time-varying and stochastic…

As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods…

Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…

Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…

Video super-resolution (VSR) aims to reconstruct a sequence of high-resolution (HR) images from their corresponding low-resolution (LR) versions. Traditionally, solving a VSR problem has been based on iterative algorithms that can exploit…

Classification of quantum data is essential for quantum machine learning and near-term quantum technologies. In this paper, we propose a new hybrid quantum-classical framework for supervised quantum learning, which we call Variational…

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…