arXiv:2608. 06419v1 Announce Type: cross Abstract: In this paper, we address the certification of datadriven feedforward control for periodic tracking of unknown nonlinear systems under partial state measurements.
arXiv:2607. 13703v1 Announce Type: new Abstract: We investigate conditional invertible neural networks (cINNs) as probabilistic inverse-dynamics models for multirotor control.
arXiv:2607. 10026v1 Announce Type: cross Abstract: This paper proposes a new notion of robust invertibility for nonlinear dynamical systems, and introduces constructive parameterizations of recurrent neural network which are robustly invertible by design.
The paper proposes using neural networks to replace the iterative force evaluation in the harmonic balance method for systems with nonlinear contacts and friction. These networks map displacement Fourier coefficients directly to nonlinear force coefficients and supply Jacobians via automatic differentiation, allowing the existing solver and continuation algorithms to remain unchanged. By learning individual nonlinear elements—such as cubic, unilateral, and Jenkins springs—under physics‑based nondimensionalization and phase normalization, a single trained network can handle a wide range of parameters, enabling a reusable library of nonlinear‑element surrogates for complex mechanical systems.
arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
The paper introduces the Physics-Informed Stochastic Configuration Machine (PI‑SCM), a backpropagation‑free neural network designed for solving nonlinear differential equations. By analytically evaluating local Jacobians, PI‑SCM linearizes the physical loss, enabling optimal weight determination through generalized linear least squares and avoiding iterative nonlinear optimization. The authors present a progressive algorithmic suite—PI‑SC‑I, PI‑SC‑II, and PI‑SC‑III—prove their universal approximation properties, and show through experiments that PI‑SCM achieves high‑fidelity predictions and parameter identification while accelerating training by orders of magnitude compared to standard PINNs.
arXiv:2501. 11655v3 Announce Type: replace-cross Abstract: This paper proposes a novel learning approach for designing Kazantzis-Kravaris or nonlinear Luenberger (KKL) observers for autonomous nonlinear systems.
arXiv:2609.25163v1 Announce Type: new Abstract: The paper proposes a novel data-driven framework for designing and training a feedback linearizing controller by explicitly incorporating relative degr...
arXiv:2606. 20417v1 Announce Type: new Abstract: Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations.
The paper introduces a linearized Physics-Informed Neural Network (lPINN), a reduced‑order neural basis approach for solving forward and inverse differential equations. In an offline phase, lPINN learns continuous, differentiable neural basis functions from numerical solutions, which are then frozen for new problem instances; the online solution is obtained by minimizing the governing‑equation residual with additional constraints. Experiments on advection‑diffusion, Burgers', and nonlinear pendulum equations show that lPINN achieves lower solution and parameter errors than vanilla PINNs while reducing online inference times by up to three orders of magnitude, and its continuous representation generalizes to finer meshes without retraining.
arXiv:2606. 15271v1 Announce Type: cross Abstract: This work presents a transparent and reproducible benchmark study of a direct dual-network Physics-Informed Neural Network (PINN) formulation for the optimal control of a mass-spring-damper system.
The paper evaluates the robustness of Physics‑Informed Neural Networks (PINNs) against noisy data in inverse problems, comparing them to a finite element method (FEM) plus optimizer baseline. Experiments on viscosity identification in 1D Burgers’ equation and 2D/3D Taylor‑Green Vortex with additive Gaussian noise show that PINNs, while requiring less human expertise, are outperformed by the traditional FEM approach in accuracy (e.g., RMSE 0.01 vs. 0.0013 for 2D Taylor‑Green with σ=1). PINNs do, however, exhibit better scaling with problem complexity, and the study highlights specific training failures that must be addressed for PINNs to become more competitive.
The paper proposes a deep learning framework that learns priors for inverse problems by exploiting the relationship between proximal operators and Hamilton–Jacobi partial differential equations. Unlike existing methods that require inverting the prior after training, this approach learns the prior directly, enabling efficient evaluation in a single forward pass. Numerical experiments demonstrate the method’s effectiveness in dimensions up to 64.