arXiv subjects

Akshay Vishwakarma

Publications and source records attributed to Akshay Vishwakarma.

2 recordsLinked to original sources

arXiv2026

Distributed Proximal Stein Variational Gradient Descent Algorithm for Large-scale Bayesian Inference in Traveltime Tomography

We present a distributed framework for large-scale Bayesian inverse problems governed by the eikonal equation, with a specific focus on seismic traveltime tomography. Traditional deterministic approaches often fail to provide the uncertainty quantification (UQ) necessary for ill-posed problems, while conventional Bayesian sampling methods such as Markov chain Monte Carlo (MCMC) suffer from the curse of dimensionality and slow convergence in high-dimensional model spaces. The proposed framework addresses these challenges through a three-tier computational strategy. First, we utilize the Fast Marching Method (FMM) to solve the eikonal equation, ensuring high numerical accuracy. Second, we reformulate the global tomographic objective into a decentralized consensus form, allowing the inversion to be decomposed into independent subproblems solved in parallel via the Alternating Direction Method of Multipliers (ADMM). This architecture eliminates the need for the explicit construction of large-scale sensitivity matrices, significantly reducing the memory footprint for 3D surveys. Finally, we integrate Stein Variational Gradient Descent (SVGD) within the ADMM workers to perform approximate posterior sampling. By evolving a set of model particles along a functional gradient direction that balances data-fitting forces with a repulsive kernel-based diversity force, we obtain an ensemble from which posterior summaries are computed. We derive a data-space Gauss-Newton update using the Woodbury matrix identity to further accelerate the particle evolution in large-scale 3D problems. Numerical experiments on complex 2D and 3D models demonstrate that the algorithm achieves stable convergence, produces high-fidelity velocity reconstructions, and provides posterior uncertainty maps.

physics.geo-ph↗

arXiv2025

Weighted Lagrange Multiplier Method for Robust Source-Independent Waveform Inversion

The Lagrange multiplier method has proven highly effective for mitigating the ill-conditioning of full waveform inversion (FWI), enabling robust and computationally efficient algorithms that converge to accurate velocity models even from poor initial estimates. Classical multiplier-based FWI methods optimize an augmented Lagrangian (AL) functional with a scalar penalty parameter that uniformly weights wave-equation constraint violations. While this balances data fit and wave-equation satisfaction, it applies uniform relaxation across the model, disregarding source locations and the natural decay of seismic energy. We propose a weighted proximal-point Lagrangian formulation that introduces spatially varying regularization, applying weaker enforcement near sources and progressively stronger enforcement with increasing distance. This compensates for the energy decay, promotes balanced wave-equation enforcement, and improves the convexity of the optimization landscape. The method also eliminates the need for explicit source signature estimation and relaxes the requirement for sources to lie on finite-difference grid points, increasing practical applicability. Enhanced computational efficiency is achieved through our dual-space ADMM implementation, which avoids repeated LU factorizations of the forward operator. Only a few LU factorizations are required, with all subsequent iterations solved via efficient forward-backward substitution, making the approach scalable to large-scale 2D and 3D problems. Numerical experiments on challenging synthetic benchmarks demonstrate that the proposed method broadens the basin of attraction of the AL objective, improves robustness to poor initial models and strong noise, and achieves faster, more stable convergence compared with standard multiplier-based methods.

physics.geo-ph↗