Scientific Machine Learning is an emerging research area focused on the
opportunities and challenges of machine learning in the context of complex
applications across science, engineering, and medicine. The most pressing
problems in these application areas have attributes that make them very
different in nature to computer science applications where data-driven
machine learning has found success.
First, these problems are typically
characterized by complex multiscale multiphysics dynamics: Small changes in
system parameters can lead to drastically large changes in system response.
Approaches that simply try to interpolate — or extrapolate — the data are
doomed to failure, no matter how expressive the underlying representation or
large the training data set. Second, these problems have high-dimensional uncertain
parameters that cannot be observed directly. When discretized, these are represented
by parameter spaces of extremely high dimension — millions or even billions of degrees
of freedom. Third, scientific and engineering data are often scarce: Experiments are costly,
time-consuming, intrusive, and sometimes dangerous. Often data are the most difficult to acquire
and are thus sparsest in the most decision-critical regions (e.g., when a system is close to failure
or close to instability). Fourth, it is often rare events (e.g., failure) that drive the most critical
decisions. It is not unusual to require design of critical engineering systems to be certified against
probabilities of failure in the range of 10-6-10-9.
Our models must provide reliable and robust predictions to support these decisions. Finally, for some
applications, such critical decisions must be made on the fly in real time,
leaving no time for re-training models on newly observed critical data.
The Center for Scientific Machine Learning is addressing these challenges through the development
of new methods that weave together the perspectives of the field of Computational Science and
Engineering — perspectives grounded in structured physics-based modeling where enforcing the
governing physical laws brings the power to constrain an otherwise intractable solution space —
and the perspectives of data-driven machine learning. Our research projects bring together a diverse
range of computing theories and algorithms, including large-scale optimization, inverse theory,
reduced-order modeling, uncertainty quantification, Bayesian inference, optimal experimental design,
data assimilation, physics-informed deep learning, interpretable machine learning, reinforcement learning, and high performance computing.