Related papers: Neural Conjugate Flows: Physics-informed architect…
To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for…
Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
This paper introduces a novel neural network - flow completion network (FCN) - to infer the fluid dynamics, includ-ing the flow field and the force acting on the body, from the incomplete data based on Graph Convolution AttentionNetwork.…
Recently normalizing flows (NFs) have demonstrated state-of-the-art performance on modeling 3D point clouds while allowing sampling with arbitrary resolution at inference time. However, these flow-based models still require long training…
Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced,…
Machine learning assisted optimal power flow (OPF) aims to reduce the computational complexity of these non-linear and non-convex constrained optimization problems by consigning expensive (online) optimization to offline training. The…
We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we…
Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…
Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…
This paper introduces, for the first time to our knowledge, physics-informed neural networks to accurately estimate the AC-OPF result and delivers rigorous guarantees about their performance. Power system operators, along with several other…
Graph convolutional networks (GCNs) are \emph{discriminative models} that directly model the class posterior $p(y|\mathbf{x})$ for semi-supervised classification of graph data. While being effective, as a representation learning approach,…
We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…
Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a…
Learning with neural networks from a continuous stream of visual information presents several challenges due to the non-i.i.d. nature of the data. However, it also offers novel opportunities to develop representations that are consistent…
Fluid dynamics spans phenomena from the Cheerios effect to cosmic evolution and has been called the 'queen mother' of science. Traditional modelling relies on numerical methods, including finite differences, volumes, and elements, that…
We are interested in learning generative models for complex geometries described via manifolds, such as spheres, tori, and other implicit surfaces. Current extensions of existing (Euclidean) generative models are restricted to specific…
This paper proposes an input convex neural network (ICNN)-Assisted optimal power flow (OPF) in distribution networks. Instead of relying purely on optimization or machine learning, the ICNN-Assisted OPF is a combination of optimization and…
Standard flow matching scales well but typically relies on an unstructured source distribution, limiting its ability to learn interpretable latent structure. Latent-variable models, by contrast, capture structure but often sacrifice…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…