arXiv:2606. 18175v1 Announce Type: cross Abstract: We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters and solved by a single direct linear least-squares QR factorization.
By Gbenga T. Awojinrin, Abdul-Akeem Olawoyin, Rami M. Younis
arXiv:2606. 02145v1 Announce Type: new Abstract: Accurate prediction of polymerization dynamics is essential for process design, control, and optimization.
By Marah Almanasreh, Alexander Mitsos, Eike Cramer
arXiv:2511. 05879v5 Announce Type: replace-cross Abstract: Hydrogen crossover is a critical safety and efficiency constraint in high-pressure polymer electrolyte membrane water electrolysis (PEMWE), but accurate prediction remains difficult because data are limited, transport physics are strongly coupled, and industrial operation requires reliable extrapolation beyond observed conditions.
By Yong-Woon Kim, Jihyeok Lee, Chulung Kang, Yung-Cheol Byun
arXiv:2608. 05892v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems.
By Yulun Wu, Matthieu Barreau, Miguel Aguiar, Karl H. Johansson
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.
By Abdeladhim Tahimi, Rinaldo Vieira da Silva Junior
arXiv:2606. 05247v1 Announce Type: new Abstract: Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints.
By Ziqian Wang, Chenxi Fang, Zhen Zhang
arXiv:2607. 00095v1 Announce Type: cross Abstract: Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics.
By Alaina Kolli, Theodoros Xenakis, Utkarsh Utkarsh, Pengfei Cai, Rafael Gomez-Bombarelli, Alan Edelman, Christopher Vincent Rackauckas
Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems. Two factors underlie this difficulty: spectral bias, the tendency of neural networks to underfit high-frequency features; and representation-coefficient coupling, the entanglement of representation learning and coefficient fitting within a single nonconvex optimization objective.
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
By Yu Liu, Jan Kronqvist, Fabricio Oliveira
arXiv:2409. 08066v3 Announce Type: replace Abstract: The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control.
By Lukas L\"uken, Sergio Lucia
arXiv:2606. 01179v1 Announce Type: cross Abstract: Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems.
By Biswajeet Sahoo, Debadutta Patra
Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks. Such problems have a natural geometric interpretation, model predictions form a manifold in data space, while the chosen parameterization can introduce parameter-effects curvature that becomes a dominant source of nonlinearity.