Home of Math + Machine Learning + X....and PINNs!

CRUNCH is the cathedral of interdisciplinary reseach 

CRUNCH supports diversity and inclusion. Has supported the MET school @PVD, [email protected], and the Association of Women in [email protected]

Math + Machine Learning + X

PINNs is the most downloaded paper in JCP

DeepOnet is the new game changer for operator regression!

George Karniadakis elected to the National Academy of Engineering (class 2022 in recognition of his contributions to engineering for “computational tools, from high-accuracy algorithms to machine learning, and applications to complex flows, stochastic processes, and microfluidics.”

George Karniadakis received the 2021 SIAM/ACM Prize in Computational Science and Engineering for “advancing spectral elements, reduced-order modeling, uncertainty quantification, dissipative particle dynamics, fractional PDEs, and scientific machine learning, while pushing applications to extreme computational scales and mentoring many leaders.”

Over 30 years of mentorship of PhD students from over 20 institutions and 10 different nationalities!

The CRUNCH group is the research team of Professor George Em Karniadakis in the Division of Applied Mathematics at Brown University. CRUNCH members have diverse interdisciplinary backgrounds, and they work at the interface of Computational Mathematics + Machine Learning + X, where X may be problems in biology, geophysics, soft matter, functional materials, physical chemistry, or fluid and solid mechanics. We welcome collaborators and visitors with bold ideas from across different fields. Our new emphasis is on Scientific Machine Learning and on PINNs that the CRUNCH group pioneered. The industry likes it (thanks ANSYS and NVIDIA), and everyone copies us shamelessly but we like it! PINNs are Physics-Informed Neural Networks and we have a whole alphabet of PINNs: cPINNs (conservative); vPINNs (variational); pPINNs (parareal); nPINNs (nonlocal); B-PINNs (Bayesian), ...You can find all the papers here.

Check-out our current research interests under Current Research.

Scientific journal covers featuring our recent works:

An atomistic fingerprint algorithm for learning ab initio molecular force fields

Understanding of the interactions between sickle cell fibers