Related papers: Modulated Neural ODEs
We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…
Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs). In the context of machine learning, differentiable solvers are central for Neural ODEs…
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…
Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…
Multi-modality spatio-temporal (MoST) data extends spatio-temporal (ST) data by incorporating multiple modalities, which is prevalent in monitoring systems, encompassing diverse traffic demands and air quality assessments. Despite…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
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…
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…
Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE…
Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each…
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…
Neural CDEs provide a natural way to process the temporal evolution of irregular time series. The number of function evaluations (NFE) is these systems' natural analog of depth (the number of layers in traditional neural networks). It is…
Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…
Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…
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…
To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…
Learning system dynamics from observations is a critical problem in many applications over various real-world complex systems, e.g., climate, ecology, and fluid systems. Recently, neural dynamics modeling method have become a prevalent…
This paper presents a machine learning framework (GP-NODE) for Bayesian systems identification from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…