7 accepted papers
In existing works on population dynamics inference, there is a focus on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamic, gradient flows are optimal in a specific sense: they minimize kinetic ener…
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly with time. The precise transition from current to next state is often modeled as the interplay of a smooth map and an explicit source of randomness. Stochastic Lifting leverages …
Deep neural networks using state space models as layers are well suited for long-range sequence tasks but can be challenging to compress after training. We use that regularizing the sum of Hankel singular values of state space models leads to a fast decay of these singular values and thus to compres…
This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the evolution of solution fields at new physics parameters and new ini…
The aim of this work is to learn models of population dynamics of physical systems that feature stochastic and mean-field effects and that depend on physics parameters. The learned models can act as surrogates of classical numerical models to efficiently predict the system behavior over the physics…
Training neural networks sequentially in time to approximate solution fields of time-dependent partial differential equations can be beneficial for preserving causality and other physics properties; however, the sequential-in-time training is numerically challenging because training errors quickly a…
Quantifying similarity between neural representations---e.g. hidden layer activation vectors---is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial…