Interacting Langevin diffusions: Gradient structure and ensemble Kalman sampler
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 …
highly desirable in many applications arising in science and engineering. In this paper we …
Achieving high accuracy with PINNs via energy natural gradient descent
J Müller, M Zeinhofer - International Conference on Machine …, 2023 - proceedings.mlr.press
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 …
Hessian-induced Riemannian metric as an optimization algorithm for physics-informed …
Variational Wasserstein gradient flow
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 …
problems over the space of probability distributions. A recent trend is to use the well-known …
Optimizing functionals on the space of probabilities with input convex neural networks
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 …
including the space of probabilities endowed with the Wasserstein metric. A typical …
Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games
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 …
solving stochastic mean-field games (MFGs). Our algorithm is geared toward high …
Efficient natural gradient descent methods for large-scale PDE-based optimization problems
L Nurbekyan, W Lei, Y Yang - SIAM Journal on Scientific Computing, 2023 - SIAM
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 …
(NGD) for a broad range of metric spaces with applications to PDE-based optimization …
High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems
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 …
spatial discretization for initial value gradient flows in generalized optimal transport metric …
Neural Wasserstein gradient flows for maximum mean discrepancies with Riesz kernels
Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-
smooth Riesz kernels show a rich structure as singular measures can become absolutely …
smooth Riesz kernels show a rich structure as singular measures can become absolutely …
Efficient gradient flows in sliced-Wasserstein space
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 …
gradient flows. To solve them numerically, a possible approach is to rely on the Jordan …