Related papers: Physics-Enforced Neural Ordinary Differential Equa…
Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging,…
Chemical kinetics plays an important role in governing the thermal evolution in reactive flows problems. The possible interactions between chemical species increase drastically with the number of species considered in the system. Various…
Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
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…
Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and…
This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…
Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In…
Classical numerical methods solve partial differential equations (PDEs) efficiently on regular meshes, but many of them become unstable on irregular domains. In practice, multiphysics interactions such as diffusion, damage, and healing…
Developing efficient and accurate algorithms for chemistry integration is a challenging task due to its strong stiffness and high dimensionality. The current work presents a deep learning-based numerical method called DeepCombustion0.0 to…
Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…
Deep residual networks (ResNets) have shown state-of-the-art performance in various real-world applications. Recently, the ResNets model was reparameterized and interpreted as solutions to a continuous ordinary differential equation or…
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…
The application of deep neural networks (DNNs) holds considerable promise as a substitute for the direct integration of chemical source terms in combustion simulations. However, challenges persist in ensuring high precision and…
Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models…
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…