Related papers: Direct Estimation of Parameters in ODE Models Usin…
In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on…
Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of…
The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
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…
The estimation law of unknown parameters vector ${\theta}$ is proposed for one class of nonlinearly parametrized regression equations $y\left( t \right) = \Omega \left( t \right)\Theta \left( \theta \right)$. We restrict our attention to…
The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential polynomials with a tension parameter that may be optimized to…
We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…
Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…
We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…
Many reaction-diffusion systems in various applications exhibit traveling wave solutions that evolve on multiple spatio-temporal scales. These traveling wave solutions are crucial for understanding the underlying dynamics of the system. In…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
Understanding and predicting complex dynamics in accelerators is necessary for their successful operation. A grand challenge in accelerator physics is to develop predictive virtual accelerators that mitigate design cost and schedule risk.…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
This study introduces a novel formulation to enhance Support Vector Machines (SVMs) in handling class imbalance and noise. Unlike the conventional Soft Margin SVM, which penalizes the magnitude of constraint violations, the proposed model…
Deep learning can accurately represent sub-grid-scale convective processes in climate models, learning from high resolution simulations. However, deep learning methods usually lack interpretability due to large internal dimensionality,…
Developing reduced-order models applicable to fluid-dynamics problems involving complex geometries and different flow conditions remains a critical challenge for turbulent flows. This study introduces VIVALDy, a novel machine-learning…
We present a differentiable weak-form learning approach for accelerating finite element simulations. Rather than introducing black-box source terms in the strong form of the governing equations, we augment the momentum equation directly in…