arXiv subjects

Mathias Louboutin

Publications and source records attributed to Mathias Louboutin.

At least 37 records · Page 2Linked to original sources

arXiv2022

Accelerating innovation with software abstractions for scalable computational geophysics

We present the SLIM (https://github.com/slimgroup) open-source software framework for computational geophysics, and more generally, inverse problems based on the wave-equation (e.g., medical ultrasound). We developed a software environment aimed at scalable research and development by designing multiple layers of abstractions. This environment allows the researchers to easily formulate their problem in an abstract fashion, while still being able to exploit the latest developments in high-performance computing. We illustrate and demonstrate the benefits of our software design on many geophysical applications, including seismic inversion and physics-informed machine learning for geophysics (e.g., loop unrolled imaging, uncertainty quantification), all while facilitating the integration of external software.

physics.comp-ph↗

arXiv2022

Velocity continuation with Fourier neural operators for accelerated uncertainty quantification

Seismic imaging is an ill-posed inverse problem that is challenged by noisy data and modeling inaccuracies -- due to errors in the background squared-slowness model. Uncertainty quantification is essential for determining how variability in the background models affects seismic imaging. Due to the costs associated with the forward Born modeling operator as well as the high dimensionality of seismic images, quantification of uncertainty is computationally expensive. As such, the main contribution of this work is a survey-specific Fourier neural operator surrogate to velocity continuation that maps seismic images associated with one background model to another virtually for free. While being trained with only 200 background and seismic image pairs, this surrogate is able to accurately predict seismic images associated with new background models, thus accelerating seismic imaging uncertainty quantification. We support our method with a realistic data example in which we quantify seismic imaging uncertainties using a Fourier neural operator surrogate, illustrating how variations in background models affect the position of reflectors in a seismic image.

physics.geo-ph↗

arXiv2022

Learned coupled inversion for carbon sequestration monitoring and forecasting with Fourier neural operators

Seismic monitoring of carbon storage sequestration is a challenging problem involving both fluid-flow physics and wave physics. Additionally, monitoring usually requires the solvers for these physics to be coupled and differentiable to effectively invert for the subsurface properties of interest. To drastically reduce the computational cost, we introduce a learned coupled inversion framework based on the wave modeling operator, rock property conversion and a proxy fluid-flow simulator. We show that we can accurately use a Fourier neural operator as a proxy for the fluid-flow simulator for a fraction of the computational cost. We demonstrate the efficacy of our proposed method by means of a synthetic experiment. Finally, our framework is extended to carbon sequestration forecasting, where we effectively use the surrogate Fourier neural operator to forecast the CO2 plume in the future at near-zero additional cost.

physics.geo-ph↗

arXiv2022

Enabling wave-based inversion on GPUs with randomized trace estimation

By building on recent advances in the use of randomized trace estimation to drastically reduce the memory footprint of adjoint-state methods, we present and validate an imaging approach that can be executed exclusively on accelerators. Results obtained on field-realistic synthetic datasets, which include salt and anisotropy, show that our method produces high-fidelity images. These findings open the enticing perspective of 3D wave-based inversion technology with a memory footprint that matches the hardware and that runs exclusively on clusters of GPUs without the undesirable need to offload certain tasks to CPUs.

physics.geo-ph↗

arXiv2021

Combining Checkpointing and Data Compression to Accelerate Adjoint-Based Optimization Problems

Seismic inversion and imaging are adjoint-based optimization problems that process up to terabytes of data, regularly exceeding the memory capacity of available computers. Data compression is an effective strategy to reduce this memory requirement by a certain factor, particularly if some loss in accuracy is acceptable. A popular alternative is checkpointing, where data is stored at selected points in time, and values at other times are recomputed as needed from the last stored state. This allows arbitrarily large adjoint computations with limited memory, at the cost of additional recomputations. In this paper, we combine compression and checkpointing for the first time to compute a realistic seismic inversion. The combination of checkpointing and compression allows larger adjoint computations compared to using only compression, and reduces the recomputation overhead significantly compared to using only checkpointing.

cs.CE↗

arXiv2021

Lossy Checkpoint Compression in Full Waveform Inversion: a case study with ZFPv0.5.5 and the Overthrust Model

This paper proposes a new method that combines check-pointing methods with error-controlled lossy compression for large-scale high-performance Full-Waveform Inversion (FWI), an inverse problem commonly used in geophysical exploration. This combination can significantly reduce data movement, allowing a reduction in run time as well as peak memory. In the Exascale computing era, frequent data transfer (e.g., memory bandwidth, PCIe bandwidth for GPUs, or network) is the performance bottleneck rather than the peak FLOPS of the processing unit. Like many other adjoint-based optimization problems, FWI is costly in terms of the number of floating-point operations, large memory footprint during backpropagation, and data transfer overheads. Past work for adjoint methods has developed checkpointing methods that reduce the peak memory requirements during backpropagation at the cost of additional floating-point computations. Combining this traditional checkpointing with error-controlled lossy compression, we explore the three-way tradeoff between memory, precision, and time to solution. We investigate how approximation errors introduced by lossy compression of the forward solution impact the objective function gradient and final inverted solution. Empirical results from these numerical experiments indicate that high lossy-compression rates (compression factors ranging up to 100) have a relatively minor impact on convergence rates and the quality of the final solution.

physics.comp-ph↗

arXiv2021

A dual formulation of wavefield reconstruction inversion for large-scale seismic inversion

Most of the seismic inversion techniques currently proposed focus on robustness with respect to the background model choice or inaccurate physical modeling assumptions, but are not apt to large-scale 3D applications. On the other hand, methods that are computationally feasible for industrial problems, such as full waveform inversion, are notoriously bogged down by local minima and require adequate starting models. We propose a novel solution that is both scalable and less sensitive to starting model or inaccurate physics when compared to full waveform inversion. The method is based on a dual (Lagrangian) reformulation of the classical wavefield reconstruction inversion, whose robustness with respect to local minima is well documented in the literature. However, it is not suited to 3D, as it leverages expensive frequency-domain solvers for the wave equation. The proposed reformulation allows the deployment of state-of-the-art time-domain finite-difference methods, and is computationally mature for industrial scale problems.

physics.geo-ph↗

arXiv2021

Compressive time-lapse seismic monitoring of carbon storage and sequestration with the joint recovery model

Time-lapse seismic monitoring of carbon storage and sequestration is often challenging because the time-lapse signature of the growth of CO2 plumes is weak in amplitude and therefore difficult to detect seismically. This situation is compounded by the fact that the surveys are often coarsely sampled and not replicated to reduce costs. As a result, images obtained for different vintages (baseline and monitor surveys) often contain artifacts that may be attributed wrongly to time-lapse changes. To address these issues, we propose to invert the baseline and monitor surveys jointly. By using the joint recovery model, we exploit information shared between multiple time-lapse surveys. Contrary to other time-lapse methods, our approach does not rely on replicating the surveys to detect time-lapse changes. To illustrate this advantage, we present a numerical sensitivity study where CO2 is injected in a realistic synthetic model. This model is representative of the geology in the southeast of the North Sea, an area currently considered for carbon sequestration. Our example demonstrates that the joint recovery model improves the quality of time-lapse images allowing us to monitor the CO2 plume seismically.

physics.geo-ph↗

arXiv2021

Ultra-low memory seismic inversion with randomized trace estimation

Inspired by recent work on extended image volumes that lays the ground for randomized probing of extremely large seismic wavefield matrices, we present a memory frugal and computationally efficient inversion methodology that uses techniques from randomized linear algebra. By means of a carefully selected realistic synthetic example, we demonstrate that we are capable of achieving competitive inversion results at a fraction of the memory cost of conventional full-waveform inversion with limited computational overhead. By exchanging memory for negligible computational overhead, we open with the presented technology the door towards the use of low-memory accelerators such as GPUs.

physics.geo-ph↗

arXiv2021

Temporal blocking of finite-difference stencil operators with sparse "off-the-grid" sources

Stencil kernels dominate a range of scientific applications, including seismic and medical imaging, image processing, and neural networks. Temporal blocking is a performance optimization that aims to reduce the required memory bandwidth of stencil computations by re-using data from the cache for multiple time steps. It has already been shown to be beneficial for this class of algorithms. However, applying temporal blocking to practical applications' stencils remains challenging. These computations often consist of sparsely located operators not aligned with the computational grid ("off-the-grid"). Our work is motivated by modeling problems in which source injections result in wavefields that must then be measured at receivers by interpolation from the grided wavefield. The resulting data dependencies make the adoption of temporal blocking much more challenging. We propose a methodology to inspect these data dependencies and reorder the computation, leading to performance gains in stencil codes where temporal blocking has not been applicable. We implement this novel scheme in the Devito domain-specific compiler toolchain. Devito implements a domain-specific language embedded in Python to generate optimized partial differential equation solvers using the finite-difference method from high-level symbolic problem definitions. We evaluate our scheme using isotropic acoustic, anisotropic acoustic, and isotropic elastic wave propagators of industrial significance. After auto-tuning, performance evaluation shows that this enables substantial performance improvement through temporal blocking over highly-optimized vectorized spatially-blocked code of up to 1.6x.

cs.DC↗

arXiv2021

Preconditioned training of normalizing flows for variational inference in inverse problems

Obtaining samples from the posterior distribution of inverse problems with expensive forward operators is challenging especially when the unknowns involve the strongly heterogeneous Earth. To meet these challenges, we propose a preconditioning scheme involving a conditional normalizing flow (NF) capable of sampling from a low-fidelity posterior distribution directly. This conditional NF is used to speed up the training of the high-fidelity objective involving minimization of the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density for indirect measurements at hand. To minimize costs associated with the forward operator, we initialize the high-fidelity NF with the weights of the pretrained low-fidelity NF, which is trained beforehand on available model and data pairs. Our numerical experiments, including a 2D toy and a seismic compressed sensing example, demonstrate that thanks to the preconditioning considerable speed-ups are achievable compared to training NFs from scratch.

stat.ML↗

arXiv2020

Scaling through abstractions -- high-performance vectorial wave simulations for seismic inversion with Devito

[Devito] is an open-source Python project based on domain-specific language and compiler technology. Driven by the requirements of rapid HPC applications development in exploration seismology, the language and compiler have evolved significantly since inception. Sophisticated boundary conditions, tensor contractions, sparse operations and features such as staggered grids and sub-domains are all supported; operators of essentially arbitrary complexity can be generated. To accommodate this flexibility whilst ensuring performance, data dependency analysis is utilized to schedule loops and detect computational-properties such as parallelism. In this article, the generation and simulation of MPI-parallel propagators (along with their adjoints) for the pseudo-acoustic wave-equation in tilted transverse isotropic media and the elastic wave-equation are presented. Simulations are carried out on industry scale synthetic models in a HPC Cloud system and reach a performance of 28TFLOP/s, hence demonstrating Devito's suitability for production-grade seismic inversion problems.

physics.comp-ph↗

arXiv2020

Time-domain Wavefield Reconstruction Inversion in a TTI medium

We introduce a generalization of time-domain wavefield reconstruction inversion to anisotropic acoustic modeling. Wavefield reconstruction inversion has been extensively researched in recent years for its ability to mitigate cycle skipping. The original method was formulated in the frequency domain with acoustic isotropic physics. However, frequency-domain modeling requires sophisticated iterative solvers that are difficult to scale to industrial-size problems and more realistic physical assumptions, such as tilted transverse isotropy, object of this study. The work presented here is based on a recently proposed dual formulation of wavefield reconstruction inversion, which allows time-domain propagator that are suitable to both large scales and more accurate physics.

physics.geo-ph↗

arXiv2020

Extended source imaging, a unifying framework for seismic & medical imaging

We present three imaging modalities that live on the crossroads of seismic and medical imaging. Through the lens of extended source imaging, we can draw deep connections among the fields of wave-equation based seismic and medical imaging, despite first appearances. From the seismic perspective, we underline the importance to work with the correct physics and spatially varying velocity fields. Medical imaging, on the other hand, opens the possibility for new imaging modalities where outside stimuli, such as laser or radar pulses, can not only be used to identify endogenous optical or thermal contrasts but that these sources can also be used to insonify the medium so that images of the whole specimen can in principle be created.

physics.geo-ph↗

arXiv2020

Architecture and performance of Devito, a system for automated stencil computation

Stencil computations are a key part of many high-performance computing applications, such as image processing, convolutional neural networks, and finite-difference solvers for partial differential equations. Devito is a framework capable of generating highly-optimized code given symbolic equations expressed in Python, specialized in, but not limited to, affine (stencil) codes. The lowering process---from mathematical equations down to C++ code---is performed by the Devito compiler through a series of intermediate representations. Several performance optimizations are introduced, including advanced common sub-expressions elimination, tiling and parallelization. Some of these are obtained through well-established stencil optimizers, integrated in the back-end of the Devito compiler. The architecture of the Devito compiler, as well as the performance optimizations that are applied when generating code, are presented. The effectiveness of such performance optimizations is demonstrated using operators drawn from seismic imaging applications.

cs.MS↗

arXiv2019

Neural network augmented wave-equation simulation

Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of Laplacian in simulation of wave equation via finite-difference method. We exploit intrinsic one-to-one similarities between timestepping algorithm with Convolutional Neural Networks (CNNs), and propose to intersperse CNNs between low-fidelity timesteps. Augmenting neural networks with low-fidelity timestepping algorithms may allow us to take large timesteps while limiting the numerical dispersion artifacts. While simulating the wave-equation with low-fidelity timestepping algorithm, by correcting the wavefield several time during propagation, we hope to limit the numerical dispersion artifact introduced by a poor discretization of the Laplacian. As a proof of concept, we demonstrate this principle by correcting for numerical dispersion by keeping the velocity model fixed, and varying the source locations to generate training and testing pairs for our supervised learning algorithm.

physics.comp-ph↗

arXiv2019

Serverless seismic imaging in the cloud

This abstract presents a serverless approach to seismic imaging in the cloud based on high-throughput containerized batch processing, event-driven computations and a domain-specific language compiler for solving the underlying wave equations. A 3D case study on Azure demonstrates that this approach allows reducing the operating cost of up to a factor of 6, making the cloud a viable alternative to on-premise HPC clusters for seismic imaging.

cs.DC↗

arXiv2019

An Event-Driven Approach to Serverless Seismic Imaging in the Cloud

Adapting the cloud for high-performance computing (HPC) is a challenging task, as software for HPC applications hinges on fast network connections and is sensitive to hardware failures. Using cloud infrastructure to recreate conventional HPC clusters is therefore in many cases an infeasible solution for migrating HPC applications to the cloud. As an alternative to the generic lift and shift approach, we consider the specific application of seismic imaging and demonstrate a serverless and event-driven approach for running large-scale instances of this problem in the cloud. Instead of permanently running compute instances, our workflow is based on a serverless architecture with high throughput batch computing and event-driven computations, in which computational resources are only running as long as they are utilized. We demonstrate that this approach is very flexible and allows for resilient and nested levels of parallelization, including domain decomposition for solving the underlying partial differential equations. While the event-driven approach introduces some overhead as computational resources are repeatedly restarted, it inherently provides resilience to instance shut-downs and allows a significant reduction of cost by avoiding idle instances, thus making the cloud a viable alternative to on-premise clusters for large-scale seismic imaging.

cs.DC↗