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Found 8 papers, 1 papers with code
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks
We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100, 000 dimensions.
Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations
We introduce an innovative approach for solving high-dimensional Fokker-Planck-L\'evy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance, and ecology.
Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity
Transformers have not been used in that capacity, and specifically, they have not been tested for solutions of PDEs with low regularity.
Two-scale Neural Networks for Partial Differential Equations with Small Parameters
We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs).
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling.
Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses
In this work, we introduce a novel integral neural operator architecture called the Peridynamic Neural Operator (PNO) that learns a nonlocal constitutive law from data.
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto space of high-order polynomials.
Knowledge-guided Semantic Computing Network
Besides, to enhance the recognition ability of the semantic tree in aspects of the diversity, randomicity and variability, we use the traditional neural network to aid the semantic tree to learn some indescribable features.
