Solving inverse problems without the use of derivatives or adjoints of the forward model is
highly desirable in many applications arising in science and engineering. In this paper we …

We propose energy natural gradient descent, a natural gradient method with respect to a
Hessian-induced Riemannian metric as an optimization algorithm for physics-informed …

Wasserstein gradient flow has emerged as a promising approach to solve optimization
problems over the space of probability distributions. A recent trend is to use the well-known …

Gradient flows are a powerful tool for optimizing functionals in general metric spaces,
including the space of probabilities endowed with the Wasserstein metric. A typical …

We present APAC-Net, an alternating population and agent control neural network for
solving stochastic mean-field games (MFGs). Our algorithm is geared toward high …

We propose efficient numerical schemes for implementing the natural gradient descent
(NGD) for a broad range of metric spaces with applications to PDE-based optimization …

We design and compute first-order implicit-in-time variational schemes with high-order
spatial discretization for initial value gradient flows in generalized optimal transport metric …

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-
smooth Riesz kernels show a rich structure as singular measures can become absolutely …

Minimizing functionals in the space of probability distributions can be done with Wasserstein
gradient flows. To solve them numerically, a possible approach is to rely on the Jordan …

We present a framework for Nesterov's accelerated gradient flows in probability space to
design efficient mean-field Markov chain Monte Carlo algorithms for Bayesian inverse …