Neural Laplace for learning Stochastic Differential Equations
This work is incremental, as it reviews the potential of an existing framework for a new application in modeling stochastic systems.
The paper explores applying the Neural Laplace framework to learn stochastic differential equations (SDEs), addressing systems influenced by randomness that cannot be modeled with ordinary differential equations, but does not report specific performance results or numbers.
Neural Laplace is a unified framework for learning diverse classes of differential equations (DE). For different classes of DE, this framework outperforms other approaches relying on neural networks that aim to learn classes of ordinary differential equations (ODE). However, many systems can't be modelled using ODEs. Stochastic differential equations (SDE) are the mathematical tool of choice when modelling spatiotemporal DE dynamics under the influence of randomness. In this work, we review the potential applications of Neural Laplace to learn diverse classes of SDE, both from a theoretical and a practical point of view.