How PeRCNN Turns Convolution Kernels into Differential Operators for Physics‑Informed Learning

PeRCNN embeds physics directly into its architecture by replacing additive nonlinearities with element‑wise multiplication in Π‑blocks, enabling convolution kernels to act as finite‑difference operators, which yields superior forward and inverse PDE solving, accurate coefficient identification, robust equation discovery, and interpretable models, as demonstrated on multiple reaction‑diffusion benchmarks.

Deep LearningPeRCNNconvolutional neural network

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How PeRCNN Turns Convolution Kernels into Differential Operators for Physics‑Informed Learning

AI Agent Research Hub

Mar 15, 2026 · Artificial Intelligence

The Forgotten Foundational Papers Behind PINNs

This article reviews the 1994 Dissanayake & Phan‑Thien and 1998 Lagaris et al. papers that first introduced feed‑forward neural networks as continuous trial functions for PDEs, contrasting their soft‑penalty and hard‑encoding boundary treatments and showing how they prefigure modern physics‑informed neural networks.

PINNsautomatic differentiationhard boundary encoding

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The Forgotten Foundational Papers Behind PINNs

AI Agent Research Hub

Feb 21, 2026 · Artificial Intelligence

Why Physics‑Informed Neural Networks (PINNs) Became a 20,000‑Citation Breakthrough

This article reviews the highly cited 2019 JCP paper that introduced Physics‑Informed Neural Networks, explains their core idea of embedding PDE residuals into the loss, compares them with contemporaneous methods, details implementation choices, showcases forward and inverse experiments, and discusses their impact, limitations, and future research directions.

Deep LearningPINNspartial differential equations

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Why Physics‑Informed Neural Networks (PINNs) Became a 20,000‑Citation Breakthrough

Model Perspective

Oct 28, 2023 · Fundamentals

Understanding the 1D Heat Conduction Equation: Derivation and Solutions

This article explains the one‑dimensional heat conduction equation, covering its basic assumptions, derivation from energy conservation, relationship between heat flux and temperature gradient, and solution methods including separation of variables and numerical techniques, while highlighting the role of initial and boundary conditions.

Physicsenergy conservationheat conduction

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Understanding the 1D Heat Conduction Equation: Derivation and Solutions