相关论文: PI-MFM: Physics-informed multimodal foundation mod…
We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…
Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…
We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…
This letter develops a novel physics-informed neural ordinary differential equations-based framework to emulate the proprietary dynamics of the inverters -- essential for improved accuracy in grid dynamic simulations. In current industry…
Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…
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…
This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for…
The present study investigates the numerical solution of Black-Scholes partial differential equation (PDE) for option valuation with multiple underlying assets. We develop a physics-informed (PI) machine learning algorithm based on a radial…
Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…
This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of…
The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…
Modeling the dynamics of real-world physical systems is critical for spatiotemporal prediction tasks, but challenging when data is limited. The scarcity of real-world data and the difficulty in reproducing the data distribution hinder…
Partial differential equations (PDEs) are widely used to describe relevant phenomena in dynamical systems. In real-world applications, we commonly need to combine formal PDE models with (potentially noisy) observations. This is especially…
The coupling of Proper Orthogonal Decomposition (POD) and deep learning-based ROMs (DL-ROMs) has proved to be a successful strategy to construct non-intrusive, highly accurate, surrogates for the real time solution of parametric nonlinear…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…