PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems
arXiv:2605.25353v1 Announce Type: new Abstract: Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields.Neural networks are well-suited for PDE parameter estimation due to their capability to model function-to-function space transformations. While existing benchmarks of machine learning methods for PDEs primarily focus on the forward problem, there are no similar comprehensive studies and benchmark datasets on PDE inverse problems, i.e., mapping solution fields to underlying physical parameter
The proliferation of neural networks and the increasing need for efficient solutions to complex scientific inverse problems are driving the development of specialized benchmarks like PDEInvBench to accelerate progress.
This development indicates a maturing field within AI, addressing a significant bottleneck in scientific and engineering simulations by providing dedicated tools for parameter estimation in PDEs, critical for real-world applications.
The availability of a comprehensive benchmark for PDE inverse problems will accelerate research and development in using AI for scientific discovery and engineering, potentially leading to faster and more accurate modeling across various disciplines.
- · AI researchers in scientific computing
- · Engineering sectors (e.g., aerospace, materials science)
- · Pharmaceutical industry (drug discovery)
- · Climate modeling
- · Traditional numerical methods (without AI integration)
- · Sectors reliant on slow, iterative manual parameter calibration
More accurate and faster identification of physical parameters in complex systems using AI.
Reduced time and cost for R&D in areas heavily dependent on PDE inverse problems, accelerating innovation.
Enhanced ability to create digital twins and predictive models for highly complex real-world phenomena, leading to optimized systems and resource allocation.
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Read at arXiv cs.LG