Deep Stochastic Residual Methods for Fully Nonlinear Parabolic Equations

arXiv:2607.16730 · math.NA, cs.NA, math.OC, stat.ML · Submitted 2026-07-18 · Read on arXiv

math.NA, cs.NA, math.OC, stat.ML

Submitted: 2026-07-18

Updated: 2026-10-19

Code: https://github.com/ZZHPKU/D2SRM

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 36× in this paper · explained in 2 episodes
• Core — 13× in this paper · explained in 2 episodes
• Consistency — 12× in this paper · explained in 3 episodes
• Benchmark — 8× in this paper · explained in 2 episodes
• Generalization — 7× in this paper · explained in 14 episodes
• Monotonicity — 5× in this paper · explained in 2 episodes
• Curse of Dimensionality — 4× in this paper · explained in 6 episodes
• Admissibility — 3× in this paper · explained in 2 episodes
• Localization — 3× in this paper · explained in 2 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Absorb — 2× in this paper · explained in 1 episode
• Actor — 2× in this paper · explained in 3 episodes
• Adam — 2× in this paper · explained in 3 episodes
• Fisher Information — 2× in this paper · explained in 4 episodes
• Fixed Point — 2× in this paper · explained in 2 episodes
• Generator — 2× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• PDE residual — 2× in this paper · explained in 2 episodes
• Universality — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 9 episodes
• Coherence — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Langevin Dynamics — 1× in this paper · explained in 3 episodes
• Neural Network Approximation — 1× in this paper · explained in 2 episodes
• Orthogonal Projection — 1× in this paper · explained in 2 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 8 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients

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