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Neural Oscillators are Universal
(2023)SAM Research ReportCoupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation learning and in physical neural networks that are used in analog ML devices. We introduce an abstract class of neural oscillators that encompasses these architectures and prove that neural oscillators are universal, i.e, they can approximate any continuous and casual operator mapping ...Report -
The Language of Hyperelastic Materials
(2024)SAM Research ReportThe automated discovery of constitutive laws forms an emerging area that focuses on automatically obtaining symbolic expressions describing the constitutive behavior of solid materials from experimental data. Existing symbolic/sparse regression methods rely on availability of libraries of material models, which are typically hand-designed by a human expert relying on known models as reference, or deploy generative algorithms with exponential ...Report -
Efficient Computation of Large-Scale Statistical Solutions to Incompressible Fluid Flows
(2024)SAM Research ReportThis work presents the development, performance analysis and subsequent optimization of a GPU-based spectral hyperviscosity solver for turbulent flows described by the three dimensional incompressible Navier-Stokes equations. The method solves for the fluid velocity fields directly in Fourier space, eliminating the need to solve a large-scale linear system of equations in order to find the pressure field. Special focus is put on the ...Report -
Vandermonde Neural Operators
(2023)SAM Research ReportFourier Neural Operators (FNOs) have emerged as very popular machine learning architectures for learning operators, particularly those arising in PDEs. However, as FNOs rely on the fast Fourier transform for computational efficiency, the architecture can be limited to input data on equispaced Cartesian grids. Here, we generalize FNOs to handle input data on non-equispaced point distributions. Our proposed model, termed as Vandermonde ...Report -
FUSE: Fast Unified Simulation and Estimation for PDEs
(2024)SAM Research ReportThe joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator learning surrogates for field prediction while using simulation-based inference (and its variants) for statistical parameter determination. Here, we argue that solving both problems within the same framework ...Report