This work presents a novel approach for adapting neural network architecture along the depth based on a posteriori error estimation. By formulating neural network training as a continuous-time optimal control problem, we derive rigorous error estimates that quantify how approximation error distributes across network layers.
arXiv:2607. 07637v1 Announce Type: new Abstract: This work presents a novel approach for adapting neural network architecture along the depth based on a posteriori error estimation.
arXiv:2606. 10682v1 Announce Type: new Abstract: While physics-informed neural networks (PINNs) have shown strong potential for process modeling, physical equations are only enforced as soft constraints during training, and thus, they do not guarantee constraint satisfaction at inference.
The paper presents a differentiable hybrid modelling framework that combines a JAX finite volume population balance solver with learnable neural network components. This approach learns constitutive laws and initial conditions directly from experimental data, improving the fidelity of transport models in chemical engineering. The framework’s differentiability also enables optimisation of experimental settings for desired process outcomes.
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
The paper presents a differentiable hybrid modelling framework that combines a JAX finite volume population balance solver with neural network components to learn constitutive laws and initial conditions directly from experimental data. This approach addresses biases from hand‑picked models and the limitations of black‑box surrogates, enabling more accurate transport predictions. The framework’s differentiability also facilitates optimisation of experimental settings for desired process outcomes.
arXiv:2409. 12707v2 Announce Type: replace-cross Abstract: Fluidic injection offers a promising solution to improve the performance of the overexpanded single expansion ramp nozzles (SERNs) during vehicle acceleration.
arXiv:2606. 02145v1 Announce Type: new Abstract: Accurate prediction of polymerization dynamics is essential for process design, control, and optimization.
arXiv:2602. 22188v2 Announce Type: replace Abstract: Modelling rock-fluid interaction requires solving a set of partial differential equations (PDEs) to predict the flow behaviour and the reactions of the fluid with the rock on the interfaces.
arXiv:2607. 23667v1 Announce Type: cross Abstract: A flow surrogate validated on a simple regime is often taken as evidence that the approach will carry to a richer one.
arXiv:2606. 16587v1 Announce Type: cross Abstract: Designing spray nozzles requires predicting how geometry shapes transient two-phase breakup, but high-fidelity volume-of-fluid (VOF) simulations with adaptive mesh refinement (AMR) are too expensive for iterative design exploration.
arXiv:2604. 23874v3 Announce Type: replace-cross Abstract: The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data.