Abstract:Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, BSDE approaches can avoid the curse of dimensionality and often admit second-order-free training objectives that do not require explicit Hessian evaluations. It has recently been established that the commonly used Euler-Maruyama (EM) time discretization induces an intrinsic bias in BSDE training losses. While high-order schemes such as Heun can fully eliminate this bias, such schemes re-introduce second-order spatial derivatives and incur substantial computational overhead. In this work, we provide a principled analysis of EM-induced loss bias and propose an unbiased, second-order-free training framework that preserves the computational advantages of BSDE methods. Our code is available at this https URL.
| Comments: | Accepted at ICML 2026 |
| Subjects: | Machine Learning (cs.LG); Numerical Analysis (math.NA); Optimization and Control (math.OC) |
| MSC classes: | 65C30, 68TO7 |
| Cite as: | arXiv:2605.14643 [cs.LG] |
| (or arXiv:2605.14643v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.14643 arXiv-issued DOI via DataCite (pending registration) |
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| Journal reference: | International Conference on Machine Learning 2026 |
Submission history
From: Jaemin Seo [view email]
[v1]
Thu, 14 May 2026 09:59:13 UTC (3,351 KB)