**Objective:** To explore the potential speedup of hybrid technologies i.e. quantum, AI and tensor networks for high-resolution seismic imaging through the [[Full Waveform Inversions]] method. ![[Pasted image 20240331232444.png]] **Project Goals:** 1. To speed up the forward problem by atleast 100x 2. To enable and harness global over local optimisation for the inverse problem **Background Context:** High Resolution Seismic Imaging through Full Waveform Inversions involves a sophisticated, very computationally intensive process. This method primarily hinges on solving thousands of Partial Differential Equations (PDEs) to accurately model the dispersion of waves in a three-dimensional subsurface environment, crucial for accurate seismic imaging applications. **Existing Workflow:** 1. Initial Guess: Formulating a starting point for seismic imaging. 2. Forward Problem: Calculating data using 3D wave propagation models. 3. Data Misfit: Comparing calculated data with measured data to identify discrepancies. 4. Inverse Problem: Refining the initial model based on the data misfit to obtain a final, more accurate model. Each iteration of this process involves a demanding forward problem, representing a 3D wave propagation challenge. Each iteration involves solving this for thousands of source point locations, typical in industrial applications, adding to the complexity. **Existing Solutions:** 1. **HPC:** The method employs HPC structures, utilizing tens of thousands of cores simultaneously. The process currently runs on HPC systems with about 50,000 cores, which constitutes approximately one-third of the machine's capacity. 2. **Algorithms:** Techniques such as domain decomposition and parallel processing are employed, especially concerning source positions. **Models** 1. **Time and Space Domain in PDEs:** The PDEs operate in both time and space domains, evolving over time. 1. The simplest model used is the acoustic wave approximation equation, involving partial time and spatial derivatives. 2. More complex models include elastic and viscoelastic approximations, adding to computational demand. 2. **Domain Geometry and Mesh Considerations**: 1. **Domain structure** typically resembles a parallel plate. 2. **Mesh smoothness** is assumed, we have continuity in the medium except for necessary discontinuities like the free surface boundary or solid interfaces. 3. **Mesh fineness** is critical, with elements typically 100 meters in size, and the number of elements reaching several hundred million, or even billions. **Inversion Problem Iteration Time:** Each iteration of the inverse problem, aimed at refining the initial model, can take around 20-30 minutes for the most complex case. This involves thousands of iterations of the wave propagation problem, each of which is also iterative in time and parallel in space. **Complexity in Moving from Acoustic to Elastic Models:** Transitioning from acoustic to elastic models increases complexity by a factor of 100. **Challenges in the Inverse Problem:** - Each wave propagation problem is costly, relying on local optimization. Mathematically, this involves solving a non-convex optimization problem, with a risk of converging to local minima that may not be geologically sensible. - The ideal scenario is a faster solution for the forward problem, facilitating global optimization – a long-sought goal hindered by computational costs. **Required Speedup:** Accelerating the forward problem by 100 times is necessary for effective global optimization. **Two Main Challenges:** 1. **Frequency and Resolution:** 1. Higher frequencies yield better resolution but increase computational demands exponentially (Frequency^4). 2. Doubling the frequency means a 16-fold increase in computational time and memory requirements, often hitting the limits of HPC capabilities. 3. Higher frequencies necessitate denser mesh and finer-scale PDE resolution. 1. **Non-linearity and Sensitivity:** 1. Non-linear nature of the inverse problem 2. Sensitivity to the starting model, typically limited to low frequencies 3. Transitioning to higher frequencies would require a larger number of degrees of freedom. **Frequency Considerations:** The frequency of the data being inverted directly impacts the detail and accuracy of the model estimation. **Potential Solution Approaches:** 1. **Global Optimisation:** Tensor Trains Optimizer (TetraOpt) as there is a potential black box nature of the underlying objective function for us to deal with or TQOpt elements that drive a smarter grid search / help with 2. **Machine Learning:** Machine Learning (TQml) framework which makes accessible the design, building, customisation, tuning, testing and benchmarking of the hybrid quantum models. Specifically Physics Informance Neural Networks (PINNs) 3. **Simulation:** TetraPDE, using our Tensor Network approaches. ![[Pasted image 20240331231409.png]]