Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network

• URL: http://arxiv.org/abs/2502.00897v1
• Date: Sun, 02 Feb 2025 20:12:39 GMT
• Title: Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network
• Authors: Shijun Cheng, Tariq Alkhalifah,
• Abstract summary: Physics-informed neural networks (PINNs) face significant challenges in modeling multi-frequency wavefields in complex velocity models. We propose Meta-LRPINN, a novel framework that combines low-rank parameterization with meta-learning and frequency embedding. Numerical experiments show that Meta-LRPINN achieves much fast convergence speed and much high accuracy compared to baseline methods.
• Score: 3.069335774032178
• License:
• Abstract: Physics-informed neural networks (PINNs) face significant challenges in modeling multi-frequency wavefields in complex velocity models due to their slow convergence, difficulty in representing high-frequency details, and lack of generalization to varying frequencies and velocity scenarios. To address these issues, we propose Meta-LRPINN, a novel framework that combines low-rank parameterization using singular value decomposition (SVD) with meta-learning and frequency embedding. Specifically, we decompose the weights of PINN's hidden layers using SVD and introduce an innovative frequency embedding hypernetwork (FEH) that links input frequencies with the singular values, enabling efficient and frequency-adaptive wavefield representation. Meta-learning is employed to provide robust initialization, improving optimization stability and reducing training time. Additionally, we implement adaptive rank reduction and FEH pruning during the meta-testing phase to further enhance efficiency. Numerical experiments, which are presented on multi-frequency scattered wavefields for different velocity models, demonstrate that Meta-LRPINN achieves much fast convergence speed and much high accuracy compared to baseline methods such as Meta-PINN and vanilla PINN. Also, the proposed framework shows strong generalization to out-of-distribution frequencies while maintaining computational efficiency. These results highlight the potential of our Meta-LRPINN for scalable and adaptable seismic wavefield modeling.

Related papers

• Deep-Unrolling Multidimensional Harmonic Retrieval Algorithms on Neuromorphic Hardware [78.17783007774295]
  This paper explores the potential of conversion-based neuromorphic algorithms for highly accurate and energy-efficient single-snapshot multidimensional harmonic retrieval. A novel method for converting the complex-valued convolutional layers and activations into spiking neural networks (SNNs) is developed. The converted SNNs achieve almost five-fold power efficiency at moderate performance loss compared to the original CNNs.
  arXiv  Detail & Related papers  (2024-12-05T09:41:33Z)
• Spatial Annealing for Efficient Few-shot Neural Rendering [73.49548565633123]
  We introduce an accurate and efficient few-shot neural rendering method named textbfSpatial textbfAnnealing regularized textbfNeRF (textbfSANeRF) By adding merely one line of code, SANeRF delivers superior rendering quality and much faster reconstruction speed compared to current few-shot neural rendering methods.
  arXiv  Detail & Related papers  (2024-06-12T02:48:52Z)
• Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model [0.0]
  We present a novel unified system that integrates a numerical solver with a deep learning component into an end-to-end framework. A stable and fast solver further allows the use of Parareal, a parallel-in-time algorithm to correct high-frequency wave components.
  arXiv  Detail & Related papers  (2024-02-04T00:07:05Z)
• GaborPINN: Efficient physics informed neural networks using multiplicative filtered networks [0.0]
  Physics-informed neural networks (PINNs) provide functional wavefield solutions represented by neural networks (NNs) We propose a modified PINN using multiplicative filtered networks, which embeds some of the known characteristics of the wavefield in training. The proposed method achieves up to a two-magnitude increase in the speed of convergence as compared with conventional PINNs.
  arXiv  Detail & Related papers  (2023-08-10T19:51:00Z)
• Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEs [86.35471039808023]
  We introduce the Incremental Fourier Neural Operator (iFNO), which progressively increases the number of frequency modes used by the model. We show that iFNO reduces total training time while maintaining or improving generalization performance across various datasets. Our method demonstrates a 10% lower testing error, using 20% fewer frequency modes compared to the existing Fourier Neural Operator, while also achieving a 30% faster training.
  arXiv  Detail & Related papers  (2022-11-28T09:57:15Z)
• Transform Once: Efficient Operator Learning in Frequency Domain [69.74509540521397]
  We study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time. This work introduces a blueprint for frequency domain learning through a single transform: transform once (T1)
  arXiv  Detail & Related papers  (2022-11-26T01:56:05Z)
• Solving Seismic Wave Equations on Variable Velocity Models with Fourier Neural Operator [3.2307366446033945]
  We propose a new framework paralleled Fourier neural operator (PFNO) for efficiently training the FNO-based solver. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models. PFNO admits higher computational efficiency on large-scale testing datasets, compared with the traditional finite-difference method.
  arXiv  Detail & Related papers  (2022-09-25T22:25:57Z)
• Wave simulation in non-smooth media by PINN with quadratic neural network and PML condition [2.7651063843287718]
  The recently proposed physics-informed neural network (PINN) has achieved successful applications in solving a wide range of partial differential equations (PDEs) In this paper, we solve the acoustic and visco-acoustic scattered-field wave equation in the frequency domain with PINN instead of the wave equation to remove source perturbation. We show that PML and quadratic neurons improve the results as well as attenuation and discuss the reason for this improvement.
  arXiv  Detail & Related papers  (2022-08-16T13:29:01Z)
• Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks [72.09574528342732]
  Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs) They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
  arXiv  Detail & Related papers  (2022-06-29T19:03:10Z)
• PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting [0.0]
  We propose a novel implementation of PINN using frequency upscaling and neuron splitting. The proposed PINN exhibits notable superiority in terms of convergence and accuracy. It can achieve neuron based high-frequency wavefield solutions with a two-hidden-layer model.
  arXiv  Detail & Related papers  (2021-09-29T16:35:50Z)
• Learning Frequency-aware Dynamic Network for Efficient Super-Resolution [56.98668484450857]
  This paper explores a novel frequency-aware dynamic network for dividing the input into multiple parts according to its coefficients in the discrete cosine transform (DCT) domain. In practice, the high-frequency part will be processed using expensive operations and the lower-frequency part is assigned with cheap operations to relieve the computation burden. Experiments conducted on benchmark SISR models and datasets show that the frequency-aware dynamic network can be employed for various SISR neural architectures.
  arXiv  Detail & Related papers  (2021-03-15T12:54:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.