Related papers: Data-driven acceleration of Photonic Simulations
Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic…
We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…
The finite-difference time-domain (FDTD) method, which is important in photonic hardware design flow, is widely adopted to solve time-domain Maxwell equations. However, FDTD is known for its prohibitive runtime cost, taking minutes to hours…
This paper proposes a two-level restricted additive Schwarz (RAS) method for multiscale PDEs, built on top of a multiscale spectral generalized finite element method (MS-GFEM). The method uses coarse spaces constructed from optimal local…
Polynomial convergence bounds are considered for left, right, and split preconditioned GMRES. They include the cases of Weighted and Deflated GMRES for a linear system Ax = b. In particular, the case of positive definite A is considered.…
We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need…
Data compression is a critical technology for large-scale plasma simulations. Storing complete particle information requires Terabyte-scale data storage, and analysis requires ad-hoc scalable post-processing tools. We propose a…
Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without…
Data-driven algorithm design is a promising, learning-based approach for beyond worst-case analysis of algorithms with tunable parameters. An important open problem is the design of computationally efficient data-driven algorithms for…
At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…
Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…
This work describes a novel simulation approach that combines machine learning and device modelling simulations. The device simulations are based on the quantum mechanical non-equilibrium Greens function (NEGF) approach and the machine…
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…
Hierarchical computational methods for multiscale mechanics such as the FE$^2$ and FE-FFT methods are generally accompanied by high computational costs. Data-driven approaches are able to speed the process up significantly by enabling to…
Finite-difference time-domain (FDTD) simulations often involve physical quantities spanning multiple orders of magnitude, such as the speed of light or electromagnetic field amplitudes. The standard practice for maintaining numerical…
In this study we develop dimension-reduction techniques to accelerate diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models (hence, CSDM): First, compress…
In this paper, we study the restarted Krylov subspace method, which is typically represented by the GMRES(m) method. Our work mainly focused on the amount of change in the iterative solution of GMRES(m) at each restart. We propose an…
Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging…
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…
In this work, a data-driven framework based on Phase-Field simulations data is proposed to highlight the capabilities of neural networks to ensure accurate low dimensionality reduction of simulated microstructural images and to provide…