Divakar Vashisth

Hoang Anh Nguyen, Divakar Vashisth, Ali Tura

Full waveform inversion (FWI) reconstructs heterogeneous material properties from receiver data but remains computationally demanding. Physics-informed neural networks (PINNs) and their domain-decomposed variants (FBPINNs) offer a mesh-free alternative but face convergence challenges when representing complex velocity fields. We present a hybrid quantum-classical FBPINN for acoustic FWI, bringing together quantum computing and classical machine learning, in which the decomposed wavefield network and the global velocity network are implemented as classical-to-quantum pipelines terminating in parameterized quantum circuits (PQCs). The PQCs are realized as differentiable JAX statevector simulators, enabling end-to-end automatic differentiation through the classical PINN, the quantum circuit, and the physics-informed loss. On a geophysical anomaly benchmark, the quantum hybrid reaches a lower L1 velocity error than the primary classical FBPINN baseline in approximately 8x fewer training iterations, despite using approximately 33% fewer trainable parameters, and it outperforms all 15 classical hyperparameter variants tested. A second benchmark (checkerboard) demonstrates the generality of the inversion pipeline, confirming that the quantum hybrid architecture can recover structured spatial variations beyond the localized anomaly benchmark. Our framework is broadly applicable to wave-based inverse problems beyond geophysics, including medical ultrasound tomography and non-destructive evaluation.

Divakar Vashisth, Tapan Mukerji

Petrophysical inversion is an important aspect of reservoir modeling. However due to the lack of a unique and straightforward relationship between seismic traces and rock properties, predicting petrophysical properties directly from seismic data is a complex task. Many studies have attempted to identify the direct end-to-end link using supervised machine learning techniques, but face different challenges such as a lack of large petrophysical training dataset or estimates that may not conform with physics or depositional history of the rocks. We present a rock and wave physics informed neural network (RW-PINN) model that can estimate porosity directly from seismic image traces with no or limited number of wells, with predictions that are consistent with rock physics and geologic knowledge of deposition. As an example, we use the uncemented sand rock physics model and normal-incidence wave physics to guide the learning of RW-PINN to eventually get good estimates of porosities from normal-incidence seismic traces and limited well data. Training RW-PINN with few wells (weakly supervised) helps in tackling the problem of non-uniqueness as different porosity logs can give similar seismic traces. We use weighted normalized root mean square error loss function to train the weakly supervised network and demonstrate the impact of different weights on porosity predictions. The RW-PINN estimated porosities and seismic traces are compared to predictions from a completely supervised model, which gives slightly better porosity estimates but poorly matches the seismic traces, in addition to requiring a large amount of labeled training data. In this paper, we demonstrate the complete workflow for executing petrophysical inversion of seismic data using self-supervised or weakly supervised rock physics informed neural networks.

Rohan Sharma, Divakar Vashisth, Bharath Shekar

Rayleigh wave dispersion curves have been widely used in near-surface studies, and are primarily inverted for the shear wave (S-wave) velocity profiles. However, the inverse problem is ill-posed, non-unique and nonlinear. Here, we introduce DispersioNET, a deep learning model based on convolution neural networks (CNN) to perform the joint inversion of Rayleigh wave fundamental and higher order mode phase velocity dispersion curves. DispersioNET is trained and tested on both noise-free and noisy dispersion curve datasets and predicts S-wave velocity profiles that match closely with the true velocities. The architecture is agnostic to variations in S-wave velocity profiles such as increasing velocity with depth and intermediate low-velocity layers, while also ensuring that the output remains independent of the number of layers.

Divakar Vashisth, Rohan Sharma, Tejas Ganesh Iyer et al.

Seismic inversion-including post-stack, pre-stack, and full waveform inversion is compute and memory-intensive. Recently, several approaches, including physics-informed machine learning, have been developed to address some of these limitations. Motivated by the potential of quantum computing, we report on our attempt to map one such classical physics-informed algorithm to a quantum framework. The primary goal is to investigate the technical challenges of this mapping, given that quantum algorithms rely on computing principles fundamentally different from those in classical computing. Quantum computers operate using qubits, which exploit superposition and entanglement, offering the potential to solve classically intractable problems. While current quantum hardware is limited, hybrid quantum-classical algorithms-particularly in quantum machine learning (QML)-demonstrate potential for near-term applications and can be readily simulated. We apply QML to subsurface imaging through the development of a hybrid quantum physics-informed neural network (HQ-PINN) for post-stack and pre-stack seismic inversion. The HQ-PINN architecture adopts an encoder-decoder structure: a hybrid quantum neural network encoder estimates P- and S-impedances from seismic data, while the decoder reconstructs seismic responses using geophysical relationships. Training is guided by minimizing the misfit between the input and reconstructed seismic traces. We systematically assess the impact of quantum layer design, differentiation strategies, and simulator backends on inversion performance. We demonstrate the efficacy of our approach through the inversion of both synthetic and the Sleipner field datasets. The HQ-PINN framework consistently yields accurate results, showcasing quantum computing's promise for geosciences and paving the way for future quantum-enhanced geophysical workflows.