arXiv:2606. 16737v1 Announce Type: cross Abstract: Engineers often measure many quantities-speed, pressure, temperature, length-expressed in different physical units.
arXiv:2607. 07863v1 Announce Type: new Abstract: In physically dominated machining processes, experimental datasets are small, expensive, and material-specific; in this regime, data curation, evaluation design, and the form of physics integration can matter as much as the learning algorithm.
arXiv:2607. 05127v1 Announce Type: cross Abstract: Understanding the physics of many-body complex dynamical systems is typically non-trivial.
arXiv:2606. 08956v1 Announce Type: new Abstract: Scientists have historically relied on mathematical models based on differential equations to relate system inputs -- forces, fluxes, or heat sources -- to outputs, such as displacement, velocity, concentration, and temperature.
arXiv:2607. 27463v1 Announce Type: new Abstract: Dimensionality Reduction (DR) is a fundamental tool for high-dimensional data exploration, reducing the complexity of latent spaces of machine learning models, and assisting in the explanation of complex opaque models.
arXiv:2607. 06348v1 Announce Type: new Abstract: We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads reconstruct individual solutions associated with different initial conditions.
arXiv:2607. 21688v1 Announce Type: cross Abstract: Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box.
arXiv:2608. 04222v1 Announce Type: cross Abstract: Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly.
arXiv:2607. 23753v1 Announce Type: new Abstract: Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system.
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.