相关论文: Gradient-free training of neural ODEs for system i…

We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…

System identification remains an intriguing challenge for lithium-ion batteries, as many models are nonlinear, exhibit multi-physics coupling, and involve a large number of parameters. In this paper, we address this challenge using the…

Bayesian experimental design (BED) for complex physical systems is often limited by the nested inference required to estimate the expected information gain (EIG) or its gradients. Each outer sample induces a different posterior, creating a…

We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…

In this study, we consider an ensemble Kalman inversion (EKI) for the numerical solution of time-fractional diffusion inverse problems (TFDIPs). Computational challenges in the EKI arise from the need for repeated evaluations of the forward…

Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…

Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…

Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…

Backpropagation dominates modern machine learning, yet it is not the only principled method for optimizing dynamical systems. We propose Kalman World Models (KWM), a class of learned state-space models trained via recursive Bayesian…

The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of…

In this paper, we introduce the Ensemble Kalman-Stein Gradient Descent (EnKSGD) class of algorithms. The EnKSGD class of algorithms builds on the ensemble Kalman filter (EnKF) line of work, applying techniques from sequential data…

We formulate the discrete-time inverse optimal control problem of inferring unknown parameters in the objective function of an optimal control problem from measurements of optimal states and controls as a nonlinear filtering problem. This…

Different approaches to using data-driven methods for subgrid-scale closure modeling have emerged recently. Most of these approaches are data-hungry, and lack interpretability and out-of-distribution generalizability. Here, we use {online}…

This paper considers the problem of data-driven robust control design for nonlinear systems, for instance, obtained when discretizing nonlinear partial differential equations (PDEs). A robust learning control approach is developed for…

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

Training Neural ODEs requires backpropagating through an ODE solve. The state-of-the-art backpropagation method is recursive checkpointing that balances recomputation with memory cost. Here, we introduce a class of algebraically reversible…

We consider optimal experimental design (OED) for nonlinear inverse problems within the Bayesian framework. Optimizing the data acquisition process for large-scale nonlinear Bayesian inverse problems is a computationally challenging task…

Neural ordinary differential equations (Neural ODEs) are a new family of deep-learning models with continuous depth. However, the numerical estimation of the gradient in the continuous case is not well solved: existing implementations of…

In this work, we propose a novel layerwise adaptive construction method for neural network architectures. Our approach is based on a goal--oriented dual-weighted residual technique for the optimal control of neural differential equations.…