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Found 21 papers, 11 papers with code
PIG: Physics-Informed Gaussians as Adaptive Parametric Mesh Representations
The approximation of Partial Differential Equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs).
Forward and Inverse Simulation of Pseudo-Two-Dimensional Model of Lithium-Ion Batteries Using Neural Networks
In this work, we address the challenges posed by the high nonlinearity of the Butler-Volmer (BV) equation in forward and inverse simulations of the pseudo-two-dimensional (P2D) model using the physics-informed neural network (PINN) framework.
Constant Acceleration Flow
Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity.
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MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data
Large language models (LLMs), like ChatGPT, have shown that even trained with noisy prior data, they can generalize effectively to new tasks through in-context learning (ICL) and pre-training techniques.
Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs
In this paper, we provide a theoretical analysis of a type of operator learning method without data reliance based on the classical finite element approximation, which is called the finite element operator network (FEONet).
Separable Physics-informed Neural Networks for Solving the BGK Model of the Boltzmann Equation
In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation.
Spectral operator learning for parametric PDEs without data reliance
In this paper, we introduce the Spectral Coefficient Learning via Operator Network (SCLON), a novel operator learning-based approach for solving parametric partial differential equations (PDEs) without the need for data harnessing.
Hydra: Multi-head Low-rank Adaptation for Parameter Efficient Fine-tuning
The recent surge in large-scale foundation models has spurred the development of efficient methods for adapting these models to various downstream tasks.
Finite Element Operator Network for Solving Elliptic-type parametric PDEs
Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance.
An Adaptive Dual-level Reinforcement Learning Approach for Optimal Trade Execution
The purpose of this research is to devise a tactic that can closely track the daily cumulative volume-weighted average price (VWAP) using reinforcement learning.
Separable Physics-Informed Neural Networks
Furthermore, we present that SPINN can solve a chaotic (2+1)-d Navier-Stokes equation significantly faster than the best-performing prior method (9 minutes vs 10 hours in a single GPU), maintaining accuracy.
Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks
SPINN operates on a per-axis basis instead of point-wise processing in conventional PINNs, decreasing the number of network forward passes.
Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs
In this paper, we perform the convergence analysis of unsupervised Legendre--Galerkin neural networks (ULGNet), a deep-learning-based numerical method for solving partial differential equations (PDEs).
Invertible Monotone Operators for Normalizing Flows
Normalizing flows model probability distributions by learning invertible transformations that transfer a simple distribution into complex distributions.
Physics-Informed Convolutional Transformer for Predicting Volatility Surface
The Black-Scholes option pricing model is one of the most widely used models by market participants.
Semi-analytic PINN methods for singularly perturbed boundary value problems
We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems.
PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers
With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs.
Unsupervised Legendre-Galerkin Neural Network for Singularly Perturbed Partial Differential Equations
Machine learning methods have been lately used to solve partial differential equations (PDEs) and dynamical systems.
Deep neural network for solving differential equations motivated by Legendre-Galerkin approximation
Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems.
Robust Neural Networks inspired by Strong Stability Preserving Runge-Kutta methods
Motivated by the SSP property and a generalized Runge-Kutta method, we propose Strong Stability Preserving networks (SSP networks) which improve robustness against adversarial attacks.
Optimal Experimental Design for Uncertain Systems Based on Coupled Differential Equations
We consider the optimal experimental design problem for an uncertain Kuramoto model, which consists of N interacting oscillators described by coupled ordinary differential equations.
