Andrew Christlieb, Taming The Curse of Dimensionality to Enable ‘First Principle’ Optimal Design in Fusion Energy

Abstract:  Recent advances at the National Ignition Facility and their achievement of thermal nuclear burn on December 5th of 2022 represents a great achievement and an exciting advancement in the state of fusion energy systems.  A close synergy between simulation, theory, and experiment, (including data assimilation) led to this advance.  However, if we were to seek to design a new device of this kind in a new operating point outside parameters covered by the experiments, we lack ‘first principle’ predictive capabilities that would enable design of such systems.  This is because inertial confined fusion systems, as well as magnetically confined fusion systems, are far from the equilibrium state and can span many plasma regimes within the device during the evolution of the plasma.  

Behind all of these challenges in building effective ‘first principle’ models is the curse of dimensionality.  To address this fundamental challenge, the Center for Hierarchical and Robust Modeling of Non-Equilibrium Transport (CHaRMNET) was created. CHaRMNET is one of only 4 DoE funded Mathematical Multifaceted Integrated Capability Centers (MMICC).  CHaRMNET seeks to develop the mathematical tools that will enable the inclusion of ‘first principle’ effects within the optimal design loop of fusion energy systems.  CHaRMNET seeks to build a first-of-its-kind holistic approach that will exploit structure within models to mitigate the curse of dimensionality and to bridge a wide range of length and time scales in plasma science. The curse of dimensionality is a critical challenge that is pervasive throughout computational science and refers to the observation that the resources needed to solve a problem on a computer scale exponentially with the dimension of the problem. Fundamental plasma models are seven-dimensional and are presently computationally intractable (with existing mathematical methods and computational resources) to drive optimization and uncertainty quantification at the engineering scale of plasma systems.

To achieve our goals, CHaRMNET has four synergistic thrusts: ‘Beyond Forward Simulation’, development of new theory for UQ and optimization with ensembles of models; ‘Multi-Scale Modeling’, development of structure preserving surrogates; ‘Simulation Acceleration’, development of structure preserving sparce representations and blended computing; and ‘Self-Consistency’, development of structure preserving and asymptotic preserving discretization’s.  In this talk, I will give an overview of these four key thrusts, and how they interact.  Next I will focus on one area, the teams work on Multi-Scale Modeling.  This will include an overview of our recent work on structure preserving ML surrogates for closure of moment expansions of kinetic systems and the outlook for this approach.  I will conclude with pointing to next steps and challenges that are on the horizon for the team.