Research map / Probabilistic and scientific modeling / Differential equations and PDEs

INEUS: Iterative Neural Solver for High-Dimensional PIDEs

NeurIPS 2026 · Probabilistic and scientific modeling › Differential equations and PDEs · approach: Neural PDE solvers · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes INEUS, a meshfree iterative neural solver for high-dimensional linear and nonlinear PIDEs that replaces jump expectations with single-jump sampled recursive regression targets, with a contraction-based convergence analysis for linear PIDEs.

Problem

Solving high-dimensional partial integro-differential equations (PIDEs) with nonlocal jump terms, where PINNs need costly numerical jump integrals and Feynman-Kac/BSDE methods only give local solutions on time grids.

Approach

Recast PIDE solving as iterated regression onto an expectation-free single-jump target G_xi with frozen weights, combined with hard-constrained PINN architecture and a Polyak-relaxed contractive operator derived from the Feynman-Kac semigroup, avoiding higher-order derivative backpropagation and jump integration.

Key results

• INEUS achieves accurate approximation of a 100-dimensional linear PIDE with jumps where standard PINNs are described as computationally intractable.
• In d=10 linear PIDE experiments, INEUS shows slightly faster convergence per epoch and substantially lower runtime than PINN, and lower MAE per runtime than the jump-adapted deep BSDE baseline.
• Hyperparameters used: alpha=0.4, h=0.5, batch size 1024, 20 inner steps, 32 gradient steps, 1000 epochs.

Surprising findings

• The residual-based PINN is reported to be more stable than INEUS, which is recursive and less stable for nonlinear function approximation.

Limitations

• Convergence proof only for linear PIDEs; nonlinear case not covered theoretically.
• Recursive approach is less stable than residual-based PINNs for nonlinear function approximation.
• Restricted to parabolic-type PIDEs in the presented analysis with smoothness assumptions.

Experimental setup

Benchmarks: 100-dimensional linear PIDE with closed-form solution 100-dimensional nonlinear HJB PIDE with MC reference 100-dimensional nonlinear Black-Scholes PIDE with Picard reference

Metrics: mean absolute error runtime loss

Baselines: PINN DGM jump-adapted deep BSDE

Builds on: physics-informed neural networks hard-constrained PINNs deep galerkin method deep BSDE method

Closest papers by meaning

• UGrid: An Efficient-And-Rigorous Neural Multigrid Solver for Linear PDEs (ICML 2024 · similarity 0.86)
• Breakeven complexity: A new perspective on neural partial differential equation solvers (NeurIPS 2026 · similarity 0.85)
• Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees (NeurIPS 2024 · similarity 0.85)
• Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries (ICML 2025 · similarity 0.85)
• Learning from Integral Losses in Physics Informed Neural Networks (ICML 2024 · similarity 0.84)
• INC: An Indirect Neural Corrector for Auto-Regressive Hybrid PDE Solvers (NeurIPS 2025 · similarity 0.84)