Related papers: Learning Nonlinear Continuous-Time Systems for For…
Uncertainty-aware deep learning (DL) models recently gained attention in fault diagnosis as a way to promote the reliable detection of faults when out-of-distribution (OOD) data arise from unseen faults (epistemic uncertainty) or the…
The distribution of a neural network's latent representations has been successfully used to detect out-of-distribution (OOD) data. This work investigates whether this distribution moreover correlates with a model's epistemic uncertainty,…
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
Ordinary differential equations have been used to model dynamical systems in a broad range. Model checking for parametric ordinary differential equations is a necessary step to check whether the assumed models are plausible. In this paper…
The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves.…
We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…
This letter presents a high-dimensional analysis of the training dynamics for a single-layer nonlinear contrastive learning model. The empirical distribution of the model weights converges to a deterministic measure governed by a…
Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different…
Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…
A high-gain extended observer is designed for a class of nonlinear uncertain systems. This observer has the ability of estimating system uncertainty, and it can be used to estimate the derivatives of signal up to order n. The controller…
Accurate overland runoff and infiltration predictions are critical for effective water resources management, in particular for urban flood management. However, the inherent uncertainty in rainfall patterns, soil properties, and initial…
Accurate trajectory prediction is essential for the safe operation of autonomous vehicles in real-world environments. Even well-trained machine learning models may produce unreliable predictions due to discrepancies between training data…
This paper proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct…
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…
We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it…