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New research details feature learning for Schrödinger equation with deep Ritz method

By PulseAugur Editorial · [2 sources] ·

This paper explores feature learning for the stationary Schrödinger equation using the deep Ritz method. It analyzes the convergence of Riemannian gradient descent, proving it reaches an approximate global minimum. The research further investigates the loss landscape when the PDE's source term follows a single-index model, demonstrating how feature alignment is achieved in both single-neuron and two-neuron scenarios. Numerical experiments validate the theory of feature emergence in the two-neuron case. AI

IMPACT This research advances techniques for solving complex differential equations, potentially impacting AI's ability to model physical systems.

RANK_REASON Academic paper detailing a novel method for solving a complex mathematical equation.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New research details feature learning for Schrödinger equation with deep Ritz method

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Academic paper detailing a novel method for solving a complex mathematical equation.
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COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Yao Yao, Yulong Lu, Gilad Lerman ·

    Feature Learning for the High Dimensional Stationary Sch\"odinger Equation with Deep Ritz Method

    arXiv:2607.06369v1 Announce Type: cross Abstract: This paper investigates feature learning within the framework of the deep Ritz method for solving the stationary Schr\"odinger equation with Neumann boundary conditions. We first analyze the convergence of Riemannian gradient desc…

  2. arXiv stat.ML TIER_1 English(EN) · Gilad Lerman ·

    Feature Learning for the High Dimensional Stationary Schödinger Equation with Deep Ritz Method

    This paper investigates feature learning within the framework of the deep Ritz method for solving the stationary Schrödinger equation with Neumann boundary conditions. We first analyze the convergence of Riemannian gradient descent in an agnostic setting, where the hypothesis fun…

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