A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients
arXiv:2606.24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging. Existing deep learning solvers often rely on repeated automatic differentiation to evaluate differential operators, which can cause instability and amplify derivative errors in high dimensions, while probabilistic methods based on stochastic representations require explicit knowledge of the data-generati
This research addresses fundamental challenges in applying deep learning to complex scientific problems, specifically high-dimensional PDEs, indicating a maturing field ready for more robust solutions.
Improving the efficiency and stability of solving high-dimensional PDEs with unknown coefficients is critical for advancing scientific machine learning applications, including reinforcement learning and other data-driven simulations.
The proposed zeroth-order deep learning method offers a way to bypass the instability and error amplification associated with traditional automatic differentiation in high-dimensional PDE solvers, potentially broadening their applicability.
- · AI researchers
- · Scientific machine learning developers
- · Industries relying on complex simulations
- · Existing deep learning methods reliant on automatic differentiation for PDEs (if
- · Traditional numerical PDE solvers (potentially challenged in certain high-dimens
More stable and efficient deep learning solutions for complex differential equations become available.
This could accelerate advances in fields like material science, climate modeling, and drug discovery where such PDEs are prevalent.
Improved simulation capabilities might lead to new scientific discoveries or optimized engineering designs at an accelerated pace.
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Read at arXiv cs.LG