AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
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Explicit integral representations for two-layer ReLU networks yield L2 approximation bounds for multivariate polynomials that depend on monomial coefficients and data distribution rather than dimension or degree.
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The physics of AI weather models
AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
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Explicit integral representations and quantitative bounds for two-layer ReLU networks
Explicit integral representations for two-layer ReLU networks yield L2 approximation bounds for multivariate polynomials that depend on monomial coefficients and data distribution rather than dimension or degree.
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