相关论文: Fast meta-solvers for 3D complex-shape scatterers …
This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed…
In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…
In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…
We present and analyze fully discrete Nystr\"om methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scattering problems by homogeneous dielectric scatterers.…
End-to-end learning has become a widely applicable and studied problem in training predictive ML models to be aware of their impact on downstream decision-making tasks. These end-to-end models often outperform traditional methods that…
An unresolved problem in Deep Learning is the ability of neural networks to cope with domain shifts during test-time, imposed by commonly fixing network parameters after training. Our proposed method Meta Test-Time Training (MT3), however,…
In this paper, we investigate the applications of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate neural…
Untrained neural networks (UNNs) offer high-fidelity electromagnetic inverse scattering reconstruction but are computationally limited by high-dimensional spatial-domain optimization. We propose a Real-Time Physics-Driven Fourier-Spectral…
Neural implicit shape representations are an emerging paradigm that offers many potential benefits over conventional discrete representations, including memory efficiency at a high spatial resolution. Generalizing across shapes with such…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
An efficient direct solver for solving the Lippmann-Schwinger integral equation modeling acoustic scattering in the plane is presented. For a problem with $N$ degrees of freedom, the solver constructs an approximate inverse in…
The three-body scattering problem in Coulombic systems is widespread, however yet unresolved problem by the mathematically rigorous methods. In this work this long term challenge has been undertaken by combining distorted waves and…
Efficient numerical solution of the acoustic Helmholtz equation in heterogeneous media remains challenging, particularly for large-scale problems with spatially-varying density - a limitation that restricts applications in biomedical…
In electromagnetism, the model of Maxwell's equations yields accurate and trustworthy predictions. Numerical solvers can reach electromagnetic solutions far beyond the set of analytical closed-form solutions; this is crucial in…
We introduce a two-layer wavelet scattering network, for object classification. This scattering transform computes a spatial wavelet transform on the first layer and a new joint wavelet transform along spatial, angular and scale variables…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
Thomson scattering (TS) diagnostics provide reliable, minimally perturbative measurements of fundamental plasma parameters, such as electron density ($n_e$) and electron temperature ($T_e$). Deep neural networks can provide accurate…
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…
Purpose: Scatter artifacts drastically degrade the image quality of cone-beam computed tomography (CBCT) scans. Although deep learning-based methods show promise in estimating scatter from CBCT measurements, their deployment in mobile CBCT…
In this paper, we propose a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. The PhaseDNN makes use of the fact that common…