A deep learning approach for computing nonequilibrium trajectories

Eric Simonnet

The analysis of rare reactive events in nonequilibrium systems without detailed balance is notoriously difficult either theoretically and computationally. These examples include phase transitions, biochemical switches, atmospheric jet transitions or even climate change, and more generally whenever these systems exhibit metastability.

After a brief introduction to Freidlin-Wentzell large-deviation theory, we will show how deep neural networks can be used to compute general Arrhenius laws and nonequilibrium/instanton trajectories. We will explore many examples from rough landscape gradient ODEs, to nongradient PDEs, including situations where nontrivial hyperbolic limit sets on the separatrix are responsible for the transitions. We will also discuss the advantage and drawbacks of using neural networks compared to classical methods.

PhD in Applied Mathematics on bifurcations analysis for PDEs, and the low-frequency variability of the mid-latitude oceanic circulation. Domains of expertise: dynamical systems theory, equilibrium and nonequilibrium statistical physics with applications to geophysical fluid flows. Computations of rare events in 2-D turbulence. More recently: machine learning approaches for solving nonequilibrium trajectories and linear/nonlinear eigenvalue problems in large dimension.