Materials Data Science and Informatics (IAS-9)

Partial Differential Equations (PDEs), which govern phenomena ranging from fluid dynamics to material stress and phase transitions, serve as the foundation of scientific modeling. Although traditional numerical solvers offer high fidelity, their significant computational cost often limits their use in applications requiring rapid iteration. Deep learning-based surrogate models provide a compelling alternative by learning to approximate the solution operator directly from data. In fields such as materials science, this acceleration enables the rapid exploration of extensive parameter spaces, facilitating the discovery of novel microstructures and the optimization of processing conditions that were previously computationally prohibitive.

The practical deployment of these surrogate models depends on their efficiency and reliability when applied beyond the training data distribution. This research prioritizes the development of efficient neural architectures and robust optimization strategies specifically designed for a wide range of PDE systems. Rather than relying on generic black-box models, the approach involves designing architectures that incorporate the underlying physics, maintaining both model efficiency and accuracy. A key aspect of this research is the investigation of the model's capacity to detect out-of-distribution (OOD) samples—cases where the physics or parameters differ substantially from the training data. Enhancing the model's awareness of its generalization boundaries ensures that these accelerated surrogates deliver more reliable predictions, avoiding overconfidence in unfamiliar scenarios.

Another central focus of this research is enhancing the adaptability of models to evolving parameter regimes. In scenarios where new physical regimes emerge sequentially, algorithms are developed to enable the surrogate model to adapt using data exclusively from the new regime. Importantly, this adaptation occurs without significantly compromising performance on previously encountered regimes, thereby addressing the challenge of catastrophic forgetting. This strategy incrementally expands the range of parameter regimes the model can address, which transforms it from a narrow specialist into a more robust generalist surrogate capable of managing an increasingly complex sequence of physical scenarios.