arXiv:2606.11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation. In this work, we construct data-driven reduced-order models that serve as structure-preserving, real-time surrogates. Remarkably, the exterior calculus that imposes physical conservation structure also exposes topological structure that we use to build a Gaussian process (GP) representation of unce
The increasing computational demands of complex simulations and the need for real-time decision-making in scientific and engineering fields necessitate more efficient and robust predictive models.
This development addresses a critical gap in scientific machine learning by providing methods for robust uncertainty quantification and structure preservation, crucial for reliability and trust in AI-driven simulations, particularly in critical infrastructure and advanced engineering.
The ability to generate near-real-time solutions to PDEs with tractable uncertainty will accelerate scientific discovery, engineering design, and operational decision-making in fields dependent on complex physical modeling.
- · Scientific machine learning researchers
- · Engineering industries
- · High-performance computing providers
- · AI developers
- · Traditional simulation software vendors (without adaptation)
- · Processes reliant on slow, computationally expensive physical simulations
Faster and more reliable scientific and engineering simulations become commonplace across various industries.
New products and services emerge that leverage real-time predictive capabilities with quantified uncertainty, leading to optimized designs and operational efficiencies.
The democratization of advanced simulation tools accelerates innovation cycles and potentially creates new markets for AI-driven design and analysis.
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Read at arXiv cs.LG