Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNs
arXiv:2603.29237v2 Announce Type: replace Abstract: Enforcing prescribed global integral constraints in mesh-free neural PDE solvers is challenging in high-dimensional domains. Existing projection methods for spatial integrals are often tied to fixed grids or uniform quadrature, which can conflict with randomly sampled physics-informed neural networks (PINNs) and scale poorly with dimension. High-order differential operators also increase reverse-mode automatic differentiation memory costs. We propose Stochastic Dimension Implicit Functional Projection (SDIFP), a quadrature-level framework for
The increasing complexity and computational demands of high-dimensional AI models necessitate more efficient and accurate numerical methods, particularly for physics-informed neural networks.
This development addresses a fundamental technical challenge in making physics-informed neural networks (PINNs) more robust and scalable, which is critical for their application in complex scientific and engineering problems.
The ability to enforce global integral conservation in high-dimensional PINNs more efficiently will expand their applicability to areas previously limited by computational cost and accuracy issues.
- · AI researchers
- · Scientific computing
- · Engineering simulations
- · Traditional numerical methods
Improved accuracy and efficiency of high-dimensional physics simulations using neural networks.
Accelerated discovery and development in fields relying on high-fidelity simulations, such as materials science or climate modeling.
Reduced time and cost for R&D in industries that heavily depend on complex simulations.
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Read at arXiv cs.LG