From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models
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 called Sparse Identification of Nonlinear Dynamics learns the governing equation as a sparse linear combination of terms in a user-defined library. ...
| Authors | Conor Rowan |
|---|---|
| Primary category | cs.LG |
| Published | 8 June 2026 |
| Last updated at source | 27 July 2026 |
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