A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent L\'evy Jumps
arXiv:2606.01122v1 Announce Type: new Abstract: We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent L\'evy jumps, targeting a general failure mode of neural PDE methods: a learned solution can match headline scalar diagnostics while miscomputing an operator inside its training loss. The protocol pairs each neural solve with at least one from-scratch independent reference, decomposes the Hamiltonian into drift, diffusion, compensator, and nonlocal-integral components across a u-grid, and compares the value function and its low-order der
The proliferation of neural network applications in complex scientific computing, especially for Partial Integro-Differential Equations (PIDEs) with Levy jumps, necessitates robust diagnostic tools to ensure reliability.
This development addresses a critical challenge in neural PDE solvers by providing a systematic protocol to diagnose and mitigate errors in complex financial or scientific models, which can otherwise lead to flawed decision-making.
The ability to accurately diagnose and validate neural network solutions for PIDEs, particularly in areas like quantitative finance, improves the trustworthiness and applicability of AI in these complex domains.
- · Quantitative finance
- · AI/ML researchers in scientific computing
- · High-frequency trading firms
- · Computational physicists
- · Methods lacking robust diagnostics
- · Investors relying on unvalidated AI models
Improved accuracy and reliability of neural network models for complex stochastic processes.
Accelerated adoption of neural PDE solvers in high-stakes applications such as derivatives pricing and risk management.
Potential for new financial products and strategies enabled by more dependable AI-driven computational models.
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Read at arXiv cs.LG