Projects
Neural Operators: AI-based solvers for PDEs
PI: Anima Anandkumar (Division of Engineering and Applied Science)
SASE: David Pitt, Scholar
Finding the numerical solutions of Partial Differential Equations (PDEs) is an important problem in scientific computing with a wide range of applications in science and engineering, including aircraft design, materials modeling, subsurface flow modeling, acoustics, quantum chemistry, electrodynamics, weather forecasting, and many more. While traditional methods based on classical numerical analysis and approximation theory have been incredibly successful in this endeavor, they remain very computationally intensive, which limits their applicability to complex engineering problems. Such methods are also unable to adapt and learn from observational data, a critical necessity for systems where the full range of physics is not understood, for example, in weather and climate modeling.
Deep learning methods have demonstrated unparalleled performance in approximating high-dimensional functions across a wide range of domains. Recently, a new deep learning paradigm, the Neural Operator (NO), was introduced that combines successful ideas from deep learning and numerical analysis for application to complex physical systems. NOs generalize neural networks to mappings between function spaces and possess similar universal approximation guarantees. This advancement allows for the design of deep learning architectures that are consistent with an underlying physical model. NOs have been used for studying turbulent flows, chaotic dynamics, materials deformations and fracture, Bayesian inverse problems, and weather forecasting, demonstrating orders of magnitude in speed-up when compared to classical methods.
While NOs have undoubtedly demonstrated potential for revolutionizing scientific computing, their software implementation remains largely academic, scattered between repositories of various researchers. The Schmidt Academy is collaborating with the Anima AI + Science Lab to develop a NO software library designed for researchers in diverse fields to easily adapt models and objectives for their use cases. Developing an open and unified framework for NOs that will seamlessly integrate across different computational architectures will allow researchers to quickly prototype models for their problems and incorporate existing machine learning solutions into their own workflows. The feedback obtained by such domain experts will in turn, accelerate the development of NOs and allow them to have a rapid impact on science and technology. Successful development of a unified NO framework will carry a long-lasting impact and be immensely beneficial to researchers and practitioners alike.
Caption: A physics-informed neural operator generates a prediction of turbulent micro-scale fluid flow in 2D. [More Information]