Machine Learning Challenges in Complex Multiscale Physical Systems

It is well-understood that traditional, single-scale, macroscopic physical models (based on conservation laws and empirical or phenomenological closures) are rapidly becoming inadequate for the accuracy requirements of modern physical, biological and engineering applications. In many cases, the macroscopic behavior of such systems arises from combined effects of multiphysics phenomena that occur over vastly different scales. While models based on first principles have the potential of offering unparalleled resolution and accuracy, their use is impractical/infeasible with current and foreseeable computational capabilities. Nevertheless, they represent a potentially valuable source of simulation data from which sufficient knowledge can be extracted in order to make predictive extrapolations over larger spatiotemporal scales.

Significant efforts have been directed towards multiscale modeling formulations which are capable of integrating models and descriptions at different scales in a manner that combines the efficiency of macroscopic models with the accuracy of microscopic models. Despite these advances, a systematic and rigorous framework for multiscale modeling that does not rely on physical insight but rather on  machine learning to “automatically” identify the number and type of macroscopic models and variables as well as deconstruct the complexity of physical models, is still missing.  

We believe  that a concerted approach is not only of paramount importance in making progress in many disciplinary applications but also necessary in enabling a new era in simulation-based analysis and design - a new approach to modeling, which functionally integrates our current and developing modeling tools with machine learning/data sciences.

The main objective of this IAS/TUM workshop is not to simply demonstrate the well understood role of data-driven science and machine learning to physical models but mainly to identify and discuss needed innovative mathematical and statistical approaches to address unique challenges that arise in predictive modelling of physical systems.

Motivated by the triptych: multiscale - data-driven - high-dimensional, and through several talks by internationally-renowned experts and roundtable-table discussions, this workshop will attempt to address fundamental  predictive modeling issues that include the following:

  • Nonparametric learning of macroscopic variables/features and their evolution (constitutive equations) from sparse high-dimensional multiphysics data
  • Developing scalable data-driven uncertainty quantification algorithms for complex multiscale/multiphysics models.
  • Learning physical invariances through data-efficient machine learning
  • Quantifying uncertainties about the structural form (“missing physics”) of macroscopic models
  • Information propagation and management across and within scales
  • Developing predictive multiscale models in problems without apparent scale separation or even with cascades of different scales
  • Statistical and optimization approaches to rare events
  • Active learning (experimental design) for training of surrogate uncertainty quantification models used in forward uncertainty propagation and inverse/design problems
  • Multiscale/Multiresolution Inverse Problems
  • High throughput algorithms for exploring the relation(s) between multiscale/multiresolution structure data with properties