From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models
arXiv:2606.08956v1 Announce Type: new Abstract: Scientists have historically relied on mathematical models based on differential equations to relate system inputs -- forces, fluxes, or heat sources -- to outputs, such as displacement, velocity, concentration, and temperature. These models rely on deep domain knowledge to determine the form of the governing differential equation, which is then calibrated with data by solving an inverse problem. In recent years, the field of Scientific Machine Learning has introduced a variety of alternative modeling strategies for physical systems. A method cal
The proliferation of AI and advanced computational methods is increasingly merging with traditional scientific modeling, leading to new paradigms for understanding complex systems.
This development allows for more accurate and efficient prediction of physical phenomena, reducing reliance on purely theoretical models and accelerating scientific discovery and engineering innovation.
The approach to scientific modeling shifts from solely inverse problem solving to integrating neural operators, enabling data-driven models to generalize and predict system behavior more effectively.
- · AI/ML researchers
- · Engineering sectors
- · Scientific computing industry
- · Advanced manufacturing
- · Traditional theoretical modeling approaches (without adaptation)
- · R&D cycles heavily reliant on physical experimentation
Scientific fields will see faster iteration and discovery cycles due to enhanced predictive capabilities.
New materials, pharmaceuticals, and engineering designs could be developed and optimized at unprecedented speeds.
This could lead to a significant acceleration in technological capabilities across numerous industries, potentially creating entirely new sectors.
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Read at arXiv cs.LG