AI RESEARCH
Stochastic Dimension Implicit Functional Projections for Exact Integral Conservation in High-Dimensional PINNs
arXiv CS.LG
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ArXi:2603.29237v1 Announce Type: new Enforcing exact macroscopic conservation laws, such as mass and energy, in neural partial differential equation (PDE) solvers is computationally challenging in high dimensions. Traditional discrete projections rely on deterministic quadrature that scales poorly and restricts mesh-free formulations like PINNs. Furthermore, high-order operators incur heavy memory overhead, and generic optimization often lacks convergence guarantees for non-convex conservation manifolds.