AI RESEARCH
M$^3$: Reframing Training Measures for Discretized Physical Simulations
arXiv CS.AI
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ArXi:2605.08843v1 Announce Type: new 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