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DRM Revisited: A Complete Error Analysis
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In this work, we address a foundational question in the theoretical analysis of the Deep Ritz Method (DRM) under the over-parameteriztion regime: Given a target precision level, how can one determine the appropriate number of training samples, the key architectural parameters of the neural networks, the step size for the projected gradient descent optimization procedure, and the requisite number of iterations, such that the output of the gradient descent process closely approximates the true solution of the underlying partial differential equation to the specified precision?
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Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks
Projected gradient descent for one-hidden-layer PINNs solving the Poisson equation is claimed to converge with average loss O(1/sqrt(T) + 1/sqrt(m)) plus an approximation error, with a generalization bound via Rademac...
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