@techreport {louboutin2021NIPSmcte,
	title = {Low-memory stochastic backpropagation with multi-channel randomized trace estimation},
	number = {TR-CSE-2021-1},
	year = {2021},
	month = {06},
	abstract = {Thanks to the combination of state-of-the-art accelerators and highly optimized open software frameworks, there has been tremendous progress in the performance of deep neural networks. While these developments have been responsible for many breakthroughs, progress towards solving large-scale problems, such as video encoding and semantic segmentation in 3D, is hampered because access to on-premise memory is often limited. Instead of relying on (optimal) checkpointing or invertibility of the network layers{\textendash}-to recover the activations during backpropagation{\textendash}-we propose to approximate the gradient of convolutional layers in neural networks with a multi-channel randomized trace estimation technique. Compared to other methods, this approach is simple, amenable to analyses, and leads to a greatly reduced memory footprint. Even though the randomized trace estimation introduces stochasticity during training, we argue that this is of little consequence as long as the induced errors are of the same order as errors in the gradient due to the use of stochastic gradient descent. We discuss the performance of networks trained with stochastic backpropagation and how the error can be controlled while maximizing memory usage and minimizing computational overhead.},
	keywords = {Convolutions, HPC, Low Memory, machine learning, randomized linear algebra},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2021/louboutin2021NIPSmcte/louboutin2021NIPSmcte.pdf},
	software = {https://github.com/slimgroup/XConv},
	author = {Mathias Louboutin and Ali Siahkoohi and Rongrong Wang and Felix J. Herrmann}
}
@techreport {siahkoohi2020TRfuqf,
	title = {Faster Uncertainty Quantification for Inverse Problems with Conditional Normalizing Flows},
	number = {TR-CSE-2020-2},
	year = {2020},
	month = {07},
	institution = {Georgia Institute of Technology},
	abstract = {In inverse problems, we often have access to data consisting of paired samples $(x,y)\sim p_X,Y(x,y)$ where $y$ are partial observations of a physical system, and $x$ represents the unknowns of the problem. Under these circumstances, we can employ supervised training to learn a solution $x$ and its uncertainty from the observations $y$. We refer to this problem as the "supervised" case. However, the data $y\sim p_Y(y)$ collected at one point could be distributed differently than observations $y{\textquoteright}\sim p_Y{\textquoteright}(y{\textquoteright})$, relevant for a current set of problems. In the context of Bayesian inference, we propose a two-step scheme, which makes use of normalizing flows and joint data to train a conditional generator $q_θ(x|y)$ to approximate the target posterior density $p_X|Y(x|y)$. Additionally, this preliminary phase provides a density function $q_θ(x|y)$, which can be recast as a prior for the "unsupervised" problem, e.g. when only the observations $y{\textquoteright}\sim p_Y{\textquoteright}(y{\textquoteright})$, a likelihood model $y{\textquoteright}|x$, and a prior on $x{\textquoteright}$ are known. We then train another invertible generator with output density $q{\textquoteright}_φ(x|y{\textquoteright})$ specifically for $y{\textquoteright}$, allowing us to sample from the posterior $p_X|Y{\textquoteright}(x|y{\textquoteright})$. We present some synthetic results that demonstrate considerable training speedup when reusing the pretrained network $q_θ(x|y{\textquoteright})$ as a warm start or preconditioning for approximating $p_X|Y{\textquoteright}(x|y{\textquoteright})$, instead of learning from scratch. This training modality can be interpreted as an instance of transfer learning. This result is particularly relevant for large-scale inverse problems that employ expensive numerical simulations.},
	keywords = {deep learning, invertible networks, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2020/siahkoohi2020TRfuqf/siahkoohi2020TRfuqf.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Philipp A. Witte and Felix J. Herrmann}
}
@techreport {louboutin2020SCsta,
	title = {Scaling through abstractions {\textendash} high-performance vectorial wave simulations for seismic inversion with Devito},
	number = {TR-CSE-2020-3},
	year = {2020},
	month = {4},
	institution = {Georgia Institute of Technology},
	abstract = {[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{\textquoteright}s suitability for production-grade seismic inversion problems.},
	keywords = {devito, elastic, finite-difference, HPC, large-scale, RTM, TTI},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2020/louboutin2020SCsta/louboutin2020SCsta.html},
	author = {Mathias Louboutin and Fabio Luporini and Philipp A. Witte and Rhodri Nelson and George Bisbas and Jan Thorbecke and Felix J. Herrmann and Gerard Gorman}
}
@techreport {witte2017TRcls,
	title = {Compressive least-squares migration with source estimation},
	number = {TR-EOAS-2017-3},
	year = {2017},
	institution = {UBC},
	abstract = {Least-squares reverse-time migration is a powerful approach for true-amplitude seismic imaging of complex geological structures. The successful application of this method is hindered by its exceedingly large computational cost and required prior knowledge of the generally unknown source wavelet. We address these problems by introducing an algorithm for low-cost sparsity-promoting least-squares migration with source estimation. We adapt a recent algorithm from sparse optimization, which allows to work with randomized subsets of shots during each iteration of least-squares migration, while still converging to an artifact-free solution. We modify the algorithm to incorporate on-the-fly source estimation through variable projection, which lets us estimate the wavelet without additional PDE solves. The algorithm is easy to implement and allows imaging at a fraction of the cost of conventional least squares reverse-time migration, requiring only around two passes trough the data, making the method feasible for large-scale imaging problems with unknown source wavelets.},
	keywords = {LSRTM, migration, source estimation, sparsity, time domain},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2017/witte2017TRcls/witte2017TRcls.html},
	author = {Philipp A. Witte and Mengmeng Yang and Felix J. Herrmann}
}
@techreport {witte2016OGHPClst,
	title = {A large-scale time-domain seismic modeling and inversion workflow in Julia},
	number = {TR-EOAS-2017-1},
	year = {2017},
	institution = {UBC},
	abstract = {We present our initial steps towards the development of a large-scale seismic modeling workflow in Julia that provides a framework for wave equation based inversion methods like full waveform inversion or least squares migration. Our framework is based on the Devito, a finite difference domain specific language compiler that generates highly optimized and parallel code. We develop a flexible workflow that is based on abstract matrixfree linear operators and enables developers to write code that closely resembles the underlying math, while at the same time leveraging highly optimized wave equation solvers, allowing us to solve large-scale three-dimensional inverse problems.},
	keywords = {HPC, inversion, Modelling},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2017/witte2016OGHPClst/witte2016OGHPClst.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Gerard Gorman and Felix J. Herrmann}
}
@techreport {witte2015TRoam,
	title = {Overview on anisotropic modeling and inversion},
	number = {TR-EOAS-2015-6},
	year = {2015},
	month = {08},
	institution = {UBC},
	abstract = {This note provides an overview on strategies for modeling and inversion with the anisotropic wave equation. Since linear and non-linear inversion methods like least squares RTM and Full Waveform Inversion depend on matching observed field data with synthetically modelled data, accounting for anisotropy effects is necessary in order to accurately match waveforms at long offsets and propagation times. In this note, the two main strategies for anisotropic modelling by solving either a pseudo acoustic wave equation or a pure quasi-P-wave equation are discussed and an inversion workflow using the pure quasi-P-wave equation is provided. In particular, we derive the exact adjoint of the anisotropic forward modelling and jacobian operator and give a detailled describtion of their implementation. The anistropic FWI workflow is tested on a sythetic data example.},
	keywords = {anisotropy, full waveform inversion, Modeling},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/witte2015TRoam/witte2015TRoam.html},
	author = {Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
@techreport {kumar2015EAGEtjm,
	title = {Time-jittered marine acquisition: low-rank v/s sparsity},
	number = {TR-EOAS-2015-2},
	year = {2015},
	month = {01},
	institution = {UBC},
	abstract = {Time-jittered simultaneous marine acquisition has been recognized as an economic way of improving the spatial sampling, and speedup acquisition, where a single (or multiple) source vessel fires at {\textendash} jittered source locations and instances in time. It has been shown in the past that this problem can be setup as a {\textendash} compressed sensing problem, where conventional seismic data is reconstructed from blended data via a sparsity-promoting optimization formulation. While the recovery quality of deblended data is very good, the recovery process is computationally very expensive. In this paper, we present a computationally efficient rank-minimization algorithm to deblend the seismic data. The proposed algorithm is suitable for large-scale seismic data, since it avoids SVD computations and uses a low-rank factorized formulation instead. Results are illustrated with simulations of time-jittered marine acquisition, which translates to jittered source locations for a given speed of the source vessel, for a single source vessel with two airgun arrays.},
	keywords = {deblending, low-rank},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/kumar2015EAGEtjm/kumar2015EAGEtjm.html},
	author = {Rajiv Kumar and Haneet Wason and Felix J. Herrmann}
}
@techreport {wang2014SEGfwi,
	title = {Full waveform inversion with interferometric measurements},
	number = {TR-EOAS-2014-5},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {In this note, we design new misfit functions for full-waveform inversion by using interferometric measurements to reduce sensitivity to phase errors. Though established within a completely different setting from the linear case, we obtain a similar observation: the interferometry can improve robustness under certain modeling errors. Moreover, in order to deal with errors on both source and receiver sides, we propose a higher order interferometry, which, as a generalization of the usual definition, involves the cross correlation of four traces. A proof of principle simulations is included on a stylized example.},
	keywords = {FWI},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/wang2014SEGfwi/wang2014SEGfwi.html},
	author = {Rongrong Wang and Ozgur Yilmaz and Felix J. Herrmann}
}
