Goal-oriented learning of stochastic differential equations using error bounds on path-space observables
arXiv:2603.20467v2 Announce Type: replace-cross Abstract: Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties. Surrogate models of the drift function of an SDE, learned from data of the high-fidelity system, are routinely used to increase the efficiency of simulation and prediction of properties. However, standard choices of loss function for learning the surrogate model fail to provide error guarantees in c
The continuous drive for more efficient and accurate AI models, especially in complex systems simulation, means advancements in underlying mathematical and computational methods are perpetually relevant.
This research addresses a fundamental limitation in current AI models for stochastic systems by providing error guarantees, which is crucial for deploying AI in high-stakes applications requiring reliability and quantifiable performance.
The ability to learn SDEs with guaranteed error bounds transforms AI applications from heuristic approximations to mathematically robust solutions, shifting perception from 'black box' to 'quantifiable risk'.
- · AI developers
- · Finance sector
- · Engineering firms
- · Scientific research institutions
- · Traditional numerical simulation methods
- · AI models without provable guarantees
More reliable and efficient AI-driven simulations for complex dynamical systems become feasible.
Increased trust and adoption of AI in critical infrastructure, climate modeling, and drug discovery due to verifiable performance.
Accelerated scientific discovery and technological innovation through AI that can credibly model and predict chaotic or complex real-world phenomena.
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Read at arXiv cs.LG