arXiv:2605.08843v2 Announce Type: replace-cross Abstract: Neural surrogate models for physical simulations are trained on discretized samples of continuous domains, where the induced empirical measure leads to uneven supervision, biasing optimization and causing spatial inconsistencies in physical fidelity. To mitigate this measure-induced bias, we propose M$^3$ (Multi-scale Morton Measure), a scalable framework that balances training measures by partitioning space according to physical variation and allocating supervision across multiple scales. Applied to three industrial-scale datasets with
The increasing complexity and scale of AI models for physical simulations require more sophisticated training methodologies to overcome inherent biases in discretized data.
Improving the accuracy and reliability of neural surrogate models directly impacts the development cycle and performance of AI-driven simulations in industrial and scientific applications.
The M$^3$ framework offers a new approach to balance training measures, potentially leading to more robust and accurate AI models for complex physical systems, reducing spatial inconsistencies.
- · AI model developers
- · Engineering and R&D sectors
- · High-performance computing providers
- · Industries relying on physical simulations
- · Traditional physical simulation methods
- · Developers of less robust AI simulation techniques
More accurate and faster AI-powered physical simulations will accelerate design, testing, and optimization processes across various industries like aerospace, automotive, and materials science.
Reduced computational costs and faster iteration cycles could democratize access to advanced simulation capabilities, fostering innovation in smaller firms and research institutions.
The ability to simulate complex physical phenomena with higher fidelity could unlock entirely new design spaces and material discoveries, leading to breakthrough technologies and products.
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