## Solving Scientific Problems with Institutional Collaborations

*George Karniadakis reflects on the power of joint appointments to drive solutions for science and engineering problems*

Named one of the top mathematicians in the world, Brown University Applied Mathematics and Engineering Professor George Karniadakis has held a joint appointment with the Computational Math group at Pacific Northwest National Laboratory (PNNL) since 2013.

“For more than 30 years, George and his research group have made huge contributions to the community by developing useful algorithms for research in industry and the national labs,” said Louis Terminello, PNNL Associate Laboratory Director, Physical and Computational Sciences. “His work at PNNL for the past 11 years has been to look at tough science and engineering problems for which computational methods don't exist or are inadequate, and try to fill this gap by developing new algorithms on high-order discretizations, uncertainty quantification, multiscale modeling, and scientific machine learning. We are grateful to have him as a part of PNNL and supporting the Lab.”

The highlight of his joint appointment has been winning three major research awards with his team in the form of Mathematical Multifaceted Integrated Capability Centers (MMICCs), Karniadakis said.

“These are multi-partner centers that PNNL leads and I am the director of,” said Karniadakis. “PNNL is the only Department of Energy laboratory with this accomplishment.”

The MMICC program has been competed three times and is funded by the Department of Energy (DOE) Advanced Scientific Computing Research program. MMICCs focus on the challenge of integrating multiple mathematical techniques, with the help of a collaborative team of partners, to find solutions for any application within the DOE mission space.

MMICCs awarded to PNNL’s Computational Math group include The Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4), Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs), and Scalable, Efficient and Accelerated Causal Reasoning Operators, Graphs and Spikes, for Earth and Embedded Systems (SEA-CROGS).

SEA-CROGS is the newest center to be awarded and focuses on physics-informed machine intelligence to analyze and predict the behavior of complex Earth systems, embedded systems, and mobile platforms.

“One of the research accomplishments that I am most proud of is the PINNs method, which has taken the world by storm and is the keystone of scientific machine learning,” said Karniadakis.

The physics-informed neural networks (PINNs), a machine learning method, was developed through PhILMs for fast solutions to scientific and engineering problems for which there was insufficient data and insufficient knowledge of physics.

“PINNs are powerful because they eliminate the tyranny of mesh generation using automatic differentiation and eliminate the need for elaborate data assimilation methods. They are also fast because they run on the new graphics processing units, which are orders of magnitude faster than central processing units,” he said.

Through his joint appointment, Karniadakis has been able to involve Brown University PhD students in research at PNNL and the MMICCs. Several of his students have since joined PNNL or gained academic tenure track positions at universities.

The key to a successful joint appointment is to “work closely with local scientists on grand problems,” said Karniadakis, “and to involve students and postdocs in joint projects.”

## About PNNL Joint Appointments

As one of the most diverse joint appointment programs among U.S. national laboratories, PNNL has partnerships with over 60 universities and research institutions. Through joint appointments, PNNL expands the research productivity and scientific impact of both PNNL and the university partners, broadening the base of expertise at each institution and helping build interdisciplinary teams to tackle tough science and technology challenges.

For more information about PNNL’s joint appointment program and the impact these leading experts are making, please visit the joint appointment website.

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Published: August 17, 2023*