arXiv Machine Learning By Ofek Aloni, Barak Fishbain

Leveraging Differentiable PDE Solvers for Semi-Neural Spatial Reconstruction From Sparse Measurements

Read the original on arXiv Machine Learning →

arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.

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arXiv Machine Learning
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Linearized PINN with pretrained nonlinear layers

The paper introduces a linearized Physics-Informed Neural Network (lPINN), a reduced‑order neural basis approach for solving forward and inverse differential equations. In an offline phase, lPINN learns continuous, differentiable neural basis functions from numerical solutions, which are then frozen for new problem instances; the online solution is obtained by minimizing the governing‑equation residual with additional constraints. Experiments on advection‑diffusion, Burgers', and nonlinear pendulum equations show that lPINN achieves lower solution and parameter errors than vanilla PINNs while reducing online inference times by up to three orders of magnitude, and its continuous representation generalizes to finer meshes without retraining.

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