A new paradigm in scientific research has been established with the integration of data-driven and physics-informed methodologies in the domain of deep learning, and it is certain to have an impact on all areas of science and engineering. This field, popularly termed "Scientific Machine Learning," relies on a known model, some (or no) high-fidelity data, and partially known constitutive relationships or closures, to be able to close the gap between the physical models and the observational data. Despite the fact that these strategies have been effective in many fields, they still face significant obstacles, such as the need for accurate and precise knowledge transmission in a data-restricted environment, and the investigation of data-driven methodologies in the century-old field of mechanics is still in its infancy. The application of deep learning techniques within the context of functional and operator regression to resolve PDEs in mechanics will be the major focus of this presentation. The approaches' extrapolation ability, accuracy, and computing efficiency in big and small data regimes, including transfer learning, would serve as indicators of their effectiveness.

Bio

Somdatta Goswami is an Assistant Professor of Research in the Division of Applied Mathematics at Brown University. Her research is focused on the development of efficient scientific machine-learning algorithms for high-dimensional physics-based systems in the fields of computational mechanics and biomechanics. After completing her Ph.D. at Bauhaus University in Germany under the supervision of Prof. Timon Rabczuk, she joined Brown University as a postdoctoral research associate under the supervision of Prof. George Karniadakis in January 2021.