Related papers: Striding Across Reynolds Numbers: Representation G…
Neural multivariate regression underpins a wide range of domains, including control, robotics, and finance, yet the geometry of its learned representations remains poorly characterized. While neural collapse has been shown to benefit…
Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction…
High-order methods and hybrid turbulence models have independently shown promise as means of decreasing the computational cost of scale-resolving simulations. The objective of this work is to develop the combination of these methods and…
We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\mathbb{R}_2$ [1] to position-orientation space $\mathbb{M}_2 \cong \mathbb{R}^2 \times S^1$. This has numerous advantages, e.g. making it possible to enhance and…
A key aspect of learned partial differential equation (PDE) solvers is that the main cost often comes from generating training data with classical solvers rather than learning the model itself. Another is that there are clear axes of…
Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural network, and the neural network parameters are calibrated to…
Large-eddy simulations (LES) and implicit LES (ILES) are wise and affordable alternatives to the unfeasible direct numerical simulations (DNS) of turbulent flows at high Reynolds numbers (Re). However, for systems with few observational…
Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering application. For many practical flows, the turbulence models are by far…
Large Eddy Simulations (LES) are becoming increasingly viable due to the growth in computational power the last few decades, and subgrid stress modelling plays a large role in the accuracy of LES. A new class of neural network models, S4…
We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-B\'enard Convection (RBC), a model for convection processes that occur in nature and industrial settings. We compare the prediction accuracy and model properties of FNO…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated…
Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physics-informed neural networks fundamentally depart from this…
It has been shown that dual encoders trained on one domain often fail to generalize to other domains for retrieval tasks. One widespread belief is that the bottleneck layer of a dual encoder, where the final score is simply a dot-product…
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…
Turbulent problems in industrial applications are predominantly solved using Reynolds Averaged Navier Stokes (RANS) turbulence models. The accuracy of the RANS models is limited due to closure assumptions that induce uncertainty into the…
In this paper we consider the Lagrangian Averaged Navier-Stokes Equations, also known as, LANS-$\alpha$ Navier-Stokes model on the two dimensional torus. We assume that the noise is a cylindrical Wiener process and its coefficient is…
When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…
We introduce novel communication strategies in synchronous distributed Deep Learning consisting of decentralized gradient reduction orchestration and computational graph-aware grouping of gradient tensors. These new techniques produce an…
We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse…