arXiv:2606.08203v1 Announce Type: cross Abstract: Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complement
The increasing complexity and scale of AI models and scientific simulations are driving demand for more efficient and stable numerical solvers.
Improved probabilistic numerical solvers can significantly accelerate progress in fields reliant on ODEs, such as AI, engineering, and physics, by enabling more accurate and stable simulations.
The development of stable and scalable probabilistic solvers for stiff and high-dimensional ODEs addresses a critical bottleneck in computational efficiency and uncertainty quantification.
- · AI researchers
- · Computational scientists
- · Engineering R&D
- · Pharmaceutical discovery
- · Legacy simulation software reliant on less efficient methods
- · Organizations with heavy reliance on manual model tuning due to solver instabili
Faster and more reliable simulation of complex systems.
Accelerated development cycles for AI models, especially those involving continuous dynamics or physical systems.
Potential for new breakthroughs in scientific discovery and engineering, previously limited by computational constraints.
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