Congratulations to Professor Jinqiao Jeffrey Duan on receiving a DOE grant in support of developing “Inertial Neural Surrogates for Stable Dynamical Prediction.” The grant award is in collaboration with Romit Maulik, research assistant professor of applied mathematics and assistant computational scientist at the Mathematics and Computer Science Division at Argonne National Laboratory. This is the first year of the project which targets “advances in modeling, analyzing, and predicting dynamical behaviors of complex systems”. More information is available in IIT’s article “Long-Term Predictions, Hold the ‘Explosions’”.
The abstract for the grant is as follows:
Experimental, observational and simulated data are noisy as well as time evolving. Stochastic dynamical systems theory and methods thus play significant roles in data science. Many DOE-relevant applications, such as those in geophysical modeling and fusion energy sciences, can benefit from building accurate, stable and efficient dynamical system surrogates from multimodal data using scientific machine learning (SciML). Many systems that arise from such applications have a large fraction of their interesting dynamics constrained to a low-dimensional manifold. However, low-dimensional data-driven dynamical system surrogates exhibit poor performance when used for long-time predictions, even when interpolations and short-time predictions seem reasonable. State-of-the-art large-scale dynamical system training relies almost entirely on cost-function minimization with simple stability promoting extensions, such as ad-hoc constraints on the Jacobian, or regularizations of the neural network, to promote smoothness. Unfortunately, these methods do not address the limited stability of data-driven surrogate models particularly in the presence of unknown adversarial perturbations, for example, when they are de-
ployed autoregressively. For long-term predictions, low stability manifests itself as solutions that explode or converge to unphysical hyperbolic sets. This project aims to address stable long-time prediction from massive datasets of high-dimensional dynamical systems. The project consists of two primary innovations:
(1) adaptive, standardized manifold discovery techniques and
(2) manifold constrained surrogate learning with enhanced stability.
The potential DOE-relevant applications of the proposed approaches include datasets related to climate and weather predictions and datasets related to fusions energy sciences.