A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent Lévy Jumps

• URL: http://arxiv.org/abs/2606.01122v1
• Date: Sun, 31 May 2026 09:44:28 GMT
• Title: A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent Lévy Jumps
• Abstract summary: We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent Lévy jumps.<n>This episode is a concrete instance of a broader neural-PDE verification failure: pointwise agreement of a learned value or control can coexist with a systematically wrong nonlocal operator.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent Lévy 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 derivatives over a (t,x) grid before any argmax comparison. Applied to a standard CRRA-Merton-Variance-Gamma benchmark, it isolates a missing 1/2-mixture factor in the neural method's importance-proposal density that scaled the nonlocal integral by exactly half - a textbook signature of a constant proposal scale error, invisible to longer training, grid refinement, and truncation sweeps. With the bug corrected, four references - two finite-difference solvers with disjoint discretizations, the neural solver, and a semi-analytic scalar baseline obtained from CRRA homogeneity - agree on the optimal control to within ~2%. The constant-coefficient CRRA benchmark collapses by homogeneity to a scalar maximization, so the scalar baseline is the efficient method here; the contribution is the protocol, applicable in principle to non-homogeneous and higher-dimensional settings where neural HJB-PIDE solvers are genuinely needed. The episode is a concrete instance of a broader neural-PDE verification failure: pointwise agreement of a learned value or control can coexist with a systematically wrong nonlocal operator, so per-component and surface-level checks are needed before trusting the argmax policy.

Related papers

• When Attribution Patching Lies: Diagnosis and a Second-Order Correction [9.338965648455238]
  We show that the dominant error stems from the non-linearities in the downstream network rather than local curvature at the patched component.<n>This insight yields three practical tools: (i) a reliability score to detect untrustworthy estimates, (ii) error bounds quantifying potential attribution mis-specifications, and (iii) a Hessian-vector-product correction that eliminates the leading-order error with only one additional backward pass.
  arXiv  Detail & Related papers  (2026-06-05T05:20:32Z)
• Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations [0.0]
  HIN-LRI is a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error.<n>A lightweight neural network, operating on a low-dimensional latent manifold, learns the residual defect that analytical methods cannot close.<n>Experiments show that HIN-LRI improves accuracy over analytical, splitting methods, and neural PDE surrogates, with stable spatial refinement, effective out-of-distribution transfer, and modest online overhead.
  arXiv  Detail & Related papers  (2026-05-06T12:50:36Z)
• Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks [0.0]
  Dual norm characterisation of weak solutions of second-order linear elliptic partial differential equations is mathematically natural but computationally intractable.<n>We prove that the $H-1$ norm of any functional is equivalent to its expected squared evaluation against a random test function whose distribution depends only on the domain.<n>This equivalence introduces the notion of weak solutions, which coincide with classical weak solutions, and motivates variational physics-informed neural networks (SV-PINNs): neural networks trained by minimising an empirical approximation of the deterministic norm of the PDE residual.
  arXiv  Detail & Related papers  (2026-05-05T09:14:38Z)
• Improving RCT-Based Treatment Effect Estimation Under Covariate Mismatch via Calibrated Alignment [0.0]
  We propose CALM, which bypasses imputation by learning embeddings that map each source's features into a common representation space.<n> OS outcome models are transferred to the RCT embedding space and calibrated using trial data, preserving causal identification from randomization.
  arXiv  Detail & Related papers  (2026-03-19T17:43:12Z)
• Verifying Closed-Loop Contractivity of Learning-Based Controllers via Partitioning [52.23804865017831]
  We address the problem of verifying closed-loop contraction in nonlinear control systems whose controller and contraction metric are both parameterized by neural networks.<n>We derive a tractable and scalable sufficient condition for closed-loop contractivity that reduces to checking that the dominant eigenvalue of a symmetric Metzler matrix is nonpositive.
  arXiv  Detail & Related papers  (2025-12-01T23:06:56Z)
• Neural PDE Solvers with Physics Constraints: A Comparative Study of PINNs, DRM, and WANs [1.131316248570352]
  Partial equations (PDEs) underpin models across science and engineering, yet analytical solutions are atypical and classical mesh-based solvers can be costly in high dimensions.<n>This dissertation presents a unified comparison of three mesh-free neural PDE solvers, physics-informed neural networks (PINNs), the deep Ritz method (DRM), and weak adversarial networks (WANs), on Poisson problems (up to 5D) and the time-independent Schr"odinger equation in 1D/2D.
  arXiv  Detail & Related papers  (2025-10-09T13:41:51Z)
• BiLO: Bilevel Local Operator Learning for PDE Inverse Problems. Part II: Efficient Uncertainty Quantification with Low-Rank Adaptation [9.229577043169224]
  Uncertainty quantification and inverse problems governed by partial differential equations (PDEs) are central to a wide range of scientific and engineering applications.<n>We extend Bilevel Local Operator Learning (BiLO) for PDE-constrained optimization problems developed in Part 1 to the Bayesian inference framework.
  arXiv  Detail & Related papers  (2025-07-22T21:20:20Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution [50.13564338607482]
  We propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix.<n>It consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module.<n>This work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Benign Overfitting in Deep Neural Networks under Lazy Training [72.28294823115502]
  We show that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification. Our results indicate that interpolating with smoother functions leads to better generalization.
  arXiv  Detail & Related papers  (2023-05-30T19:37:44Z)
• Greedy based Value Representation for Optimal Coordination in Multi-agent Reinforcement Learning [64.05646120624287]
  We derive the expression of the joint Q value function of LVD and MVD. To ensure optimal consistency, the optimal node is required to be the unique STN. Our method outperforms state-of-the-art baselines in experiments on various benchmarks.
  arXiv  Detail & Related papers  (2022-11-22T08:14:50Z)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.