Related papers: Neural Ordinary Differential Equation Control of D…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient,…

Modeling continuous-time dynamics constitutes a foundational challenge, and uncovering inter-component correlations within complex systems holds promise for enhancing the efficacy of dynamic modeling. The prevailing approach of integrating…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

Semantic image understanding is a challenging topic in computer vision. It requires to detect all objects in an image, but also to identify all the relations between them. Detected objects, their labels and the discovered relations can be…

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…

The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…

Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…

Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem,…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

Accurate forecasting of energy demand and supply is critical for optimizing sustainable energy systems, yet it is challenged by the variability of renewable sources and dynamic consumption patterns. This paper introduces a neural framework…

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…

The uncertainty in human driving behaviors leads to stop-and-go instabilities in freeway traffic. The traffic dynamics are typically modeled by the Aw-Rascle-Zhang (ARZ) Partial Differential Equation (PDE) models, in which the relaxation…

Neural Ordinary Differential Equations model dynamical systems with ODEs learned by neural networks. However, ODEs are fundamentally inadequate to model systems with long-range dependencies or discontinuities, which are common in…

Neural networks with physics based inductive biases such as Lagrangian neural networks (LNN), and Hamiltonian neural networks (HNN) learn the dynamics of physical systems by encoding strong inductive biases. Alternatively, Neural ODEs with…

The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned…