@conference {park2025ML4SEISMICftn,
	title = {Fisher-Informed Training of Neural Operators for Reliable PDE Inversion},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Neural operators have shown strong performance for PDE-solution learning; however, their effectiveness in PDE-constrained optimization, such as inversion, remains limited, in part because inaccurately learned derivatives can mislead gradient-based updates. Standard training typically optimizes only the forward least-squares fit, so during iterative inversion the optimization variable can drift outside the training distribution, further degrading quality of derivative information and inversion performance. To address this limitation, we propose a training algorithm designed for inversion: the surrogate is trained not only to predict forward outputs but also to learn observation-relevant gradients, which leads to Fisher-information directed parameter updates. We evaluate forward and gradient accuracy, as well as the inversion trajectory, on problems governed by PDEs{\textemdash}Darcy flow and laminar (incompressible) Navier{\textendash}Stokes{\textemdash}which are relevant to porous-media fluid flow and energy-storage applications. Our results suggest that training for gradient fidelity with forward accuracy unlocks a pathway to reliable, efficient, neural operator{\textendash}based inversion.},
	keywords = {deep learning, derivatve-informed, Fisher-information, FNO, GCS, Inverse problems, ML4SEISMIC, permeability, reduced-order modeling, reservoir simulation, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/park2025ML4SEISMICftn},
	author = {Jeongjin Park and Grant Bruer and Huseyin Tuna Erdinc and Richard Rex Arockiasamy and Nisha Chandramoorthy and Felix J. Herrmann}
}
@conference {park2025IMAGErdn,
	title = {A reduced-order derivative-informed neural operator for subsurface fluid-flow},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {deep learning, derivatve-informed, Fisher-information, FNO, GCS, IMAGE, Inverse problems, permeability, reduced-order modeling, reservoir simulation, SEG, Uncertainty quantification},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/park2025IMAGErdn/IMAGE_Jayjay.pdf},
	author = {Jeongjin Park and Grant Bruer and Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {park2025ML4SEISMICvmb,
	title = {Velocity Model Building with Jacobian-Informed Neural Operators},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	keywords = {deep learning, derivatve-informed, FNO, GCS, Inverse problems, ML4SEISMIC, permeability, reduced-order modeling, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/park2025ML4SEISMICvmb},
	author = {Jeongjin Park and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@conference {witte2021JULIACONmedlj,
	title = {InvertibleNetworks.jl - Memory efficient deep learning in Julia},
	booktitle = {JuliaCon},
	year = {2021},
	note = {(JuliaCon, virtual)},
	month = {07},
	abstract = {We present InvertibleNetworks.jl, an open-source package for invertible neural networks and normalizing flows using memory-efficient backpropagation. InvertibleNetworks.jl uses manually implement gradients to take advantage of the invertibility of building blocks, which allows for scaling to large-scale problem sizes. We present the architecture and features of the library and demonstrate its application to a variety of problems ranging from loop unrolling to uncertainty quantification.},
	keywords = {deep learning, Invertible network, Julia, Normalizing flows, segmentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/JuliaCon/2021/witte2021JULIACONmedlj/witte2021JULIACONmedlj.pdf},
	url2 = {https://www.youtube.com/watch?v=9M-zEGHY4i4},
	author = {Philipp A. Witte and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Bas Peters and Felix J. Herrmann}
}
@conference {peters2019SIAMGEOgmrip,
	title = {Generalized Minkowski sets for the regularization of inverse problems},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2019},
	note = {(SIAM)},
	month = {05},
	abstract = {We present a new algorithm to compute projections onto the intersection of constraint sets, designed particularly for multiple sets because we exploit similarities between constraint sets. When we do not know projections onto the individual sets in closed form, as is the case for total-variation constraints, our algorithm does not need other optimization algorithms to solve sub-problems. This a significant advantage in terms of computational cost and number of tuning parameters and stopping conditions, compared to classical algorithms to compute projections onto the intersection, such as Dykstra{\textquoteright}s algorithm. The proposed algorithm is suitable for problems with a large number of model parameters such as full-waveform inversion because it exploits coarse and fine-grained parallelism, and we also present a multilevel accelerated version. The corresponding software is open-source and implemented in Julia. We present strategies to use projections onto multiple constraints to regularize full-waveform inversion for models with salt domes or sedimentary geology.},
	keywords = {Intersections, Inverse problems, Minkowski set, Projections, Sets},
	url = {https://www.pathlms.com/siam/courses/11267/sections/14618/video_presentations/128671},
	url2 = {https://meetings.siam.org/sess/dsp_talk.cfm?p=97656},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {peters2019SEGans,
	title = {A numerical solver for least-squares sub-problems in 3D wavefield reconstruction inversion and related problem formulations},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2019},
	note = {(SEG, San Antonio)},
	month = {09},
	pages = {1536-1540},
	abstract = {Recent years saw a surge of interest in seismic waveform inversion approaches based on quadratic-penalty or augmented-Lagrangian methods, including Wavefield Reconstruction Inversion. These methods typically need to solve a least-squares sub-problem that contains a discretization of the Helmholtz equation. Memory requirements for direct solvers are often prohibitively large in three dimensions, and this limited the examples in the literature to two dimensions. We present an algorithm that uses iterative Helmholtz solvers as a black-box to solve the least-squares problem corresponding to 3D grids. This algorithm enables Wavefield Reconstruction Inversion and related formulations, in three dimensions. Our new algorithm also includes a root-finding method to convert a penalty into a constraint on the data-misfit without additional computational cost, by reusing precomputed quantities. Numerical experiments show that the cost of parallel communication and other computations are small compared to the main cost of solving one Helmholtz problem per source and one per receiver.},
	keywords = {Full-waveform inversion, least-squares, numerical linear algebra, penalty method, quadratic constraints, root finding, SEG},
	doi = {10.1190/segam2019-3216638.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/peters2019SEGans/peters2019SEGans.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/peters2019SEGans/peters2019SEGans_pres.pdf},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {peters2018CMSWMissrip,
	title = {Intersections and sums of sets for the regularization of inverse problems},
	booktitle = {Canadian Mathematical Society Winter Meeting},
	year = {2018},
	note = {(CMSWM)},
	month = {12},
	abstract = {We present new algorithms to compute projections onto the intersection of constraint sets. We focus on problems with multiple sets for which there is no simple and closed-form projection. Different from more classical methods such as Dykstra{\textquoteright}s algorithm, we do not need other algorithms to solve sub-problems. Our algorithms are based on the alternating direction method of multipliers and apply to models/images/video on small 2D and large 3D grids because we exploit computational similarity between constraint sets, coarse and fine-grained parallelism, and we also present a multilevel accelerated version. To obtain more flexible descriptions of prior knowledge, we introduce a formulation that allows constraint sets to be the sum of intersections of sets, which is essentially an extension of a Minkowski set. This formulation builds on the success of additive image descriptions that are usually based on penalty methods, such as cartoon-texture decomposition and robust principal component analysis. We show applications where we use multiple constraint sets to regularize partial-differential-equation based parameter estimation problems such as seismic waveform inversion, as well as various image and video processing and segmentation tasks.},
	keywords = {Intersections, Inverse problems, Projections, Sets},
	url = {https://cms.math.ca/Events/winter18/abs/ipi$\#$bp},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {herrmann2016SEGWScvp,
	title = {Constraints versus penalties for edge-preserving full-waveform inversion},
	booktitle = {SEG Workshop on Where are we heading with FWI; Dallas},
	year = {2016},
	note = {(SEG Workshop, Dallas)},
	month = {10},
	abstract = {Full-waveform inversion is arguably one of the most challenging inverse problems out there. For this reason, it is remarkable that so much progress has been made over the years. While we can look back with confidence at an increasing number of success stories, the application of full-waveform technologies to deeper targets and complex geologies remains challenging making it an expensive proposition. So far, efforts to overcome some of these challenges have mainly been directed towards extended formulations such as Symes{\textquoteright}s and Biondi{\textquoteright}s subsurface offset/rau-parameters, Mike Warner/Lluis Guasch{\textquoteright}s Wiener filters in their adaptive full-waveform inversion, and van Leeuwen/Herrmann{\textquoteright}s Wavefield Reconstruction Inversion, where the wave-equation appears as a least-squares term in the objective. While this recent work {\textendash}- including other approaches such as different data-misfit objective functions {\textendash}- has removed some of FWI cycle-skip issues it does, with the exception perhaps of box constraints, not incorporate rudimentary information on the geology on the unknown model. Following recent work by Ernie Esser, we present a general framework how to incorporate this type of information in the form of constraints. Contrary to Tikhonov-like regularization or gradient filtering, imposing constraints has several key advantages, namely (i) they can be expressed in simple human understandable terms such as lower and upper limits for the velocity without the necessity to introduce additional parameters and assumptions on the probability distribution of the model; (ii) they can consist of several constraints, e.g. box and smoothness constraints, as long as their intersection in non-empty; and (iii) they can be imposed in a separate inner loop, which does not affect gradients and Hessians of full-waveform inversion itself. By means of examples, we will demonstrate the advocacy of constrained formulations as they apply to full-waveform inversion. This is joint work with Bas Peters.},
	keywords = {Full-waveform inversion, SEG, workshop},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/herrmann2016SEGWScvp/herrmann2016SEGWScvp_pres.pdf},
	author = {Felix J. Herrmann and Bas Peters}
}
@conference {lange2016dtg,
	title = {Devito: Towards a generic finite difference DSL using symbolic python},
	booktitle = {6th Workshop on Python for High-Performance and Scientific Computing},
	year = {2016},
	note = {(PyHPC, Utah)},
	month = {11},
	pages = {67-75},
	abstract = {Domain specific languages (DSL) have been used in a variety of fields to express complex scientific problems in a concise manner and provide automated performance optimization for a range of computational architectures. As such DSLs provide a powerful mechanism to speed up scientific Python computation that goes beyond traditional vectorization and pre-compilation approaches, while allowing domain scientists to build applications within the comforts of the Python software ecosystem. In this paper we present Devito, a new finite difference DSL that provides optimized stencil computation from high-level problem specifications based on symbolic Python expressions. We demonstrate Devito{\textquoteright}s symbolic API and performance advantages over traditional Python acceleration methods before highlighting its use in the scientific context of seismic inversion problems.},
	keywords = {acoustic, finite differences, HPC, inversion, Modelling, python, software optimization},
	doi = {10.1109/PyHPC.2016.9},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/PyHPC/2016/lange2016dtg/lange2016dtg.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/PyHPC/2016/lange2016dtg/lange2016dtg_pres.pdf},
	author = {Michael Lange and Navjot Kukreja and Mathias Louboutin and Fabio Luporini and Felippe Vieira Zacarias and Vincenzo Pandolfo and Paulius Velesko and Paulius Kazakas and Gerard Gorman}
}
@conference {peters2016SEGprs,
	title = {Parallel reformulation of the sequential adjoint-state method},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {1411-1415},
	abstract = {This abstract is about reducing the total computation time to solve full-waveform inversion problems. A common problem formulation is a nonlinear least-squares problem where the gradient is computed using the adjoint-state algorithm. This formulation offers parallelism for the computation of gradients for different sources and frequencies. The adjoint-state algorithm itself is sequential however and this is a limiting factor when a lot of compute nodes are available and only a few wavefields need to be computed. This situation occurs when stochastic optimization strategies are used to minimize the objective function. We present a parallel reformulation of the sequential adjoint-state algorithm, which allows the forward- and adjoint wavefields to be computed in parallel. Both algorithms are mathematically equivalent but the parallel version is twice as fast in run time. An important characteristic of the proposed algorithm is that one wavefield needs to be computed per source and one per receiver. These fields can be used to apply the (inverse) Gauss-Newton Hessian to a vector without recomputing wavefields. A 2D example shows that good full-waveform inversion results are obtained, even when a small number of sources and receivers is used.},
	keywords = {FWI, numerical linear algebra, parallel computing, PDE-constrained optimization, SEG},
	doi = {10.1190/segam2016-13966771.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/peters2016SEGprs/peters2016SEGprs.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/peters2016SEGprs/peters2016SEGprs_pres.pdf},
	author = {Bas Peters and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {peters2015PRECONasl,
	title = {An algorithm for solving least-squares problems with a Helmholtz block and multiple right-hand-sides},
	booktitle = {International Conference On Preconditioning Techniques For Scientific And Industrial Applications},
	year = {2015},
	note = {(PRECON, The Netherlands)},
	month = {06},
	keywords = {CGMN, Helmholtz, least-squares, matrix-free, randomized linear algebra},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/PRECON/2015/peters2015PRECONasl/peters2015PRECONasl_pres.pdf},
	author = {Bas Peters and Chen Greif and Felix J. Herrmann}
}
@conference {smithyman2015EAGEcwi,
	title = {Constrained waveform inversion of colocated VSP and surface seismic data},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {Constrained Full-Waveform Inversion (FWI) is applied to produce a high-resolution velocity model from both Vertical Seismic Profiling (VSP) and surface seismic data. The case study comes from the Permian Basin in Texas, USA. This dataset motivates and tests several new developments in methodology that enable recovery of model results that sit within multiple a priori constraint sets. These constraints are imposed through a Projected Quasi-Newton (PQN) approach, wherein the projection set is the intersection of physical property bounds and anisotropic wavenumber filtering. This enables the method to recover geologically-reasonable models while preserving the fast model convergence offered by a quasi-Newton optimization scheme like l-BFGS. In the Permian Basin example, low-frequency data from both arrays are inverted together and regularized by this projection approach. Careful choice of the constraint sets is possible without requiring tradeoff parameters as in a quadratic penalty approach to regularization. Multiple 2D FWI results are combined to produce an interpolated 3D model that is consistent with the models from migration velocity analysis and VSP processing, while offering improved resolution and illumination of features from both datasets.},
	keywords = {EAGE, VSP, waveform inversion},
	doi = {10.3997/2214-4609.201412906},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/smithyman2015EAGEcwi/smithyman2015EAGEcwi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/smithyman2015EAGEcwi/smithyman2015EAGEcwi_pres.pdf},
	author = {Brendan R. Smithyman and Bas Peters and Felix J. Herrmann}
}
@conference {peters2015SIAMmfq,
	title = {Matrix-free quadratic-penalty methods for PDE-constrained optimization},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2015},
	note = {(SIAM, Salt Lake City)},
	month = {03},
	abstract = {The large scale of seismic waveform inversion makes matrix free implementations essential. We show how to exploit the quadratic penalty structure to construct matrix free reduced-space and full-space algorithms, which have some advantages over the commonly used Lagrangian based methods for PDE-constrained optimization. This includes the construction of effective and sparse Hessian approximations and reduced sensitivity to the initial guess. A computational bottleneck is the need to solve a large least squares problem with a PDE block. When direct solvers are not available, we propose a fast matrix free iterative approach with reasonable memory requirements. It takes advantage of the structure of the least squares problem with a combination of preconditioning, low rank decomposition and deflation.},
	keywords = {least-squares, low-rank, PDE-constrained optimization, quadratic-penalty, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2015/peters2015SIAMmfq/peters2015SIAMmfq.pdf},
	author = {Bas Peters and Felix J. Herrmann and Chen Greif}
}
@conference {herrmann2015SIAMpcf,
	title = {Pros and cons of full- and reduced-space methods for Wavefield Reconstruction Inversion},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2015},
	note = {(SIAM Conference on Mathematical and Computational Issues in the Geosciences, Stanford University, California)},
	month = {06-07},
	abstract = {By insisting on fitting observed data, Wavefield Reconstruction Inversion (WRI) is no longer cycle skipped and therefore less reliant on the accuracy of starting models. While extending the search space mitigates local minima, there are challenges scaling to 3D seismic when using reduced-space methods that require accurate solves. Conversely, full-space methods allow for inaccurate solves but require storage of all wavefields. We weigh pros and cons of these two approaches in the seismic context.},
	keywords = {FWI, SIAM, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2015/herrmann2015SIAMpcf/herrmann2015SIAMpcf_pres.pdf},
	author = {Felix J. Herrmann and Bas Peters}
}
@conference {louboutin2015IIPFWIrwi,
	title = {Regularizing waveform inversion by projections onto convex sets},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function and does not require significant additional computation. The method is demonstrated on the inversion of the 2D marine isotropic elastic synthetic seismic benchmark by Chevron using an acoustic modeling code. To highlight the effect of the projections, we apply no data pre-processing. This is joint work with Bas Peters.},
	keywords = {convex, FWI, regularization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/louboutin2015IIPFWIrwi/louboutin2015IIPFWIrwi_pres.pdf},
	author = {Mathias Louboutin and Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@conference {peters2015SEGWSsew,
	title = {Simultaneous estimation of wavefields and medium parameters - reduced-space versus full-space waveform inversion},
	booktitle = {SEG Workshop on The Limit of FWI in Subsurface Parameter Recovery; New Orleans},
	year = {2015},
	note = {(SEG, New Orleans)},
	month = {10},
	keywords = {full-space, PDE-constrained optimization, quadratic penalty method, SEG, waveform inversion, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2015/peters2015SEGWSsew/peters2015SEGWSsew_pres.pdf},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {peters2015AIPwri,
	title = {Wavefield-reconstruction inversion},
	booktitle = {Conference on Applied Inverse Problems},
	year = {2015},
	note = {(AIP, Helsinki)},
	month = {05},
	abstract = {Wavefield Reconstruction Inversion is a method for PDE-constrained optimization, which revolves around the estimation of fields using the PDE as well as the observed data in a least-squares sense. The method is quadratic penalty based, which offers some interesting possibilities for the construction of algorithms, compared to the Lagrangian form. One of the main benefits of the method is when the initial guess is far from the global minimizer. Reduced-space and full-space algorithms are discussed, including illustrative examples. The method was developed with seismic applications in mind, but applies to other PDE-constrained optimization problems as well.},
	keywords = {AIP, Full-waveform inversion, Optimization, penalty method, Waveform reconstruction inversion},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/AIP/2015/peters2015AIPwri/peters2015AIPwri.pdf},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {petrenko2014EAGEaih,
	title = {Accelerating an iterative Helmholtz solver with FPGAs},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {We implement the Kaczmarz row-projection algorithm (Kaczmarz (1937)) on a CPU host + FPGA accelerator platform using techniques of dataflow programming. This algorithm is then used as the preconditioning step in CGMN, a modified version of the conjugate gradients method (Bj{\"o}rck and Elfving (1979)) that we use to solve the time-harmonic acoustic isotropic constant density wave equation. Using one accelerator we achieve a speed-up of over 2{\texttimes} compared with one Intel core.},
	keywords = {CGMN, EAGE, FPGA, Helmholtz equation, Kaczmarz, reconfigurable computing},
	doi = {10.3997/2214-4609.20141141},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/petrenko2014EAGEaih/petrenko2014EAGEaih.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/petrenko2014EAGEaih/petrenko2014EAGEaih_pres.pdf},
	author = {Art Petrenko and Tristan van Leeuwen and Diego Oriato and Simon Tilbury and Felix J. Herrmann}
}
@conference {petrenko2014OGHPCaih,
	title = {Accelerating an iterative Helmholtz solver with FPGAs},
	booktitle = {OGHPC},
	year = {2014},
	month = {03},
	abstract = {We implement the Kaczmarz row-projection algorithm [Kaczmarz, 1937] on a CPU host + FPGA accelerator platform using techniques of dataflow programming. This algorithm is then used as the preconditioning step in CGMN, a modified version of the conjugate gradients method [Bj?rck and Elfving, 1979] that we use to solve the time-harmonic acoustic isotropic constant density wave equation.},
	keywords = {CGMN, FPGA, Helmholtz equation, Kaczmarz, OGHPC, reconfigurable computing},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/OGHPC/2014/petrenko2014OGHPCaih/petrenko2014OGHPCaih.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/OGHPC/2014/petrenko2014OGHPCaih/petrenko2014OGHPCaih_poster.pdf},
	author = {Art Petrenko and Felix J. Herrmann and Diego Oriato and Simon Tilbury and Tristan van Leeuwen}
}
@conference {lago2014CMCCRMN,
	title = {CRMN method for solving time-harmonic wave equation},
	booktitle = {Copper Mountain Conference},
	year = {2014},
	note = {(Copper Mountain)},
	month = {04},
	abstract = {We address the solution of PDEs associated with the wave propagation phenomena in heterogeneous media using CGMN method. It consists of a conjugate gradients method using Kaczmarz double sweeps as preconditioner. This preconditioner has the property of {\textquoteleft}{\textquoteleft}symmetrizing" the problem allowing short recursion and Lanczos type of Krylov methods to be employed. In this talk we propose the use of CR, a minimal residual Krylov method closely related to CG. We study the proposed method which we call CRMN and discuss crucial aspects as the behaviour of the norm of the residual and the norm of the true error. We also discuss the result of an inversion of a small subsample of the 3D velocity model SEG/EAGE Overthrust using frugal full-waveform inversion method with CRMN and CGMN for solving the associated PDE, showing a strong interest in studying the behaviour of CRMN for larger realistic cases.},
	keywords = {CGMN, CRMN, Forward Modelling, Helmholtz equation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CMC/2014/lago2014CMCCRMN.pdf},
	author = {Rafael Lago and Art Petrenko and Zhilong Fang and Felix J. Herrmann}
}
@conference {lago2014EAGEfst,
	title = {Fast solution of time-harmonic wave-equation for full-waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {For many full-waveform inversion techniques, the most computationally intensive step is the computation of a numerical solution for the wave equation on every iteration. In the frequency domain approach, this requires the solution of very large, complex, sparse, ill-conditioned linear systems. In this extended abstract we bring out attention specifically to CGMN method for solving PDEs, known for being flexible (i.e. it is able to treat equally acoustic data as well as visco-elastic or more complex scenarios) efficient with respect both to memory and computation time, and controllable accuracy of the final approximation. We propose an improvement for the known CGMN method by imposing a minimal residual condition, which incurs in one extra model vector storage. The resulting algorithm called CRMN enjoys several interesting properties as monotonically nonincreasing behaviour of the norm of the residual and minimal residual, guaranteeing optimal convergence for the relative residual criterion. We discuss numerical experiments both in an isolated PDE solve and also within the inversion procedure, showing that in a realistic scenario we can expect a speedup around 25\% when using CRMN rather than CGMN.},
	keywords = {CGMN, CRMN, EAGE, FWI, Time-Harmonic Wave Equation},
	doi = {10.3997/2214-4609.20140812},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/lago2014EAGEfst/lago2014EAGEfst.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/lago2014EAGEfst/lago2014EAGEfst_pres.pdf},
	author = {Rafael Lago and Art Petrenko and Zhilong Fang and Felix J. Herrmann}
}
@conference {leeuwen2014EAGEntf,
	title = {A new take on FWI: wavefield reconstruction inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {We discuss a recently proposed novel method for waveform inversion: Wavefield Reconstruction Inversion (WRI). As opposed to conventional FWI {\textendash} which attempts to minimize the error between observed and predicted data obtained by solving a wave equation {\textendash} WRI reconstructs a wave-field from the data and extracts a model-update from this wavefield by minimizing the wave-equation residual. The method does not require explicit computation of an adjoint wavefield as all the necessary information is contained in the reconstructed wavefield. We show how the corresponding model updates can be interpreted physically analogously to the conventional imaging-condition-based approach.},
	keywords = {EAGE, Full-waveform inversion, Optimization, penalty method, Wavefield Reconstruction Inversion},
	doi = {10.3997/2214-4609.20140703},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/leeuwen2014EAGEntf/leeuwen2014EAGEntf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/leeuwen2014EAGEntf/leeuwen2014EAGEntf_pres.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann and Bas Peters}
}
@conference {peters2014SEGsrh,
	title = {A sparse reduced Hessian approximation for multi-parameter wavefield reconstruction inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2014},
	note = {(SEG)},
	month = {10},
	pages = {1206-1210},
	abstract = {Multi-Parameter full-waveform inversion is a challenging problem, because the unknown parameters appear in the same wave equation and the magnitude of the parameters can vary many orders of magnitude. This makes accurate estimation of multiple-parameters very difficult. To mitigate the problems, sequential strategies, regularization methods and scalings of gradients and quasi-Newton Hessians have been proposed. All of these require design, fine-tuning and adaptation to different waveform inversion problems. We propose to use a sparse approximation to the Hessian derived from a penalty-formulation of the objective function. Sparseness allows to have the Hessian in memory and compute update directions at very low cost. This results in decent reconstruction of the multiple parameters at very low additional memory and computational expense.},
	keywords = {Full-waveform inversion, Hessian, Optimization, penalty method, SEG},
	doi = {http://dx.doi.org/10.1190/segam2014-1667.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/peters2014SEGsrh/peters2014SEGsrh.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/peters2014SEGsrh/peters2014SEGsrh_pres.pdf},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {peters2014EAGEweb,
	title = {Wave-equation based inversion with the penalty method: adjoint-state versus wavefield-reconstruction inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {In this paper we make a comparison between wave-equation based inversions based on the adjoint-state and penalty methods. While the adjoint-state method involves the minimization of a data-misfit and exact solutions of the wave-equation for the current velocity model, the penalty-method aims to first find a wavefield that jointly fits the data and honours the physics, in a least-squares sense. Given this reconstructed wavefield, which is a proxy for the true wavefield in the true model, we calculate updates for the velocity model. Aside from being less nonlinear{\textendash}the acoustic wave equation is linear in the wavefield and model parameters but not in both{\textendash}the inversion is carried out over a solution space that includes both the model and the wavefield. This larger search space allows the algortihm to circumnavigate local minima, very much in the same way as recently proposed model extentions try to acomplish. We include examples for low frequencies, where we compare full-waveform inversion results for both methods, for good and bad starting models, and for high frequencies where we compare reverse-time migration with linearized imaging based on wavefield-reconstruction inversion. The examples confirm the expected benefits of the proposed method.},
	keywords = {EAGE, Full-waveform inversion, Imaging, Optimization, penalty method},
	doi = {10.3997/2214-4609.20140704},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/peters2014EAGEweb/peters2014EAGEweb.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/peters2014EAGEweb/peters2014EAGEweb_pres.pdf},
	author = {Bas Peters and Felix J. Herrmann and Tristan van Leeuwen}
}
@conference {herrmann2014SEGWS,
	title = {Wavefield Reconstruction Inversion (WRI) {\textendash} a new take on wave-equation based inversion},
	booktitle = {SEG Workshop on Full Waveform Inversion - Elastic Approaches and Issues with Anisotropy, Nonshallow Inversion, Poor Starting Model; Denver},
	year = {2014},
	note = {(SEG Workshop, Denver)},
	month = {10},
	keywords = {FWI, SEG, workshop, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/herrmann2014SEGWSwri/herrmann2014SEGWSwri_pres.pdf},
	author = {Felix J. Herrmann and Ernie Esser and Tristan van Leeuwen and Bas Peters}
}
@conference {petrenko2013HPCSsaoc,
	title = {Software acceleration of CARP, an iterative linear solver and preconditioner},
	year = {2013},
	month = {06},
	publisher = {HPCS},
	organization = {HPCS},
	abstract = {We present the results of software optimization of a row-wise preconditioner (Component Averaged Row Projections) for the method of conjugate gradients, which is used to solve the diagonally banded Helmholtz system representing frequency domain, isotropic acoustic seismic wave simulation. We demonstrate that in our application, a preconditioner bound to one processor core and accessing memory contiguously reduces execution time by 7\% for matrices having on the order of 108 non-zeros. For reference we note that our C implementation is over 80 times faster than the corresponding code written for a high-level numerical analysis language.},
	keywords = {frequency-domain, Helmholtz equation, HPCS, Kaczmarz, software, wave propagation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/HPCS/2013/petrenko2013HPCSsaoc/petrenko2013HPCSsaoc.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/HPCS/2013/petrenko2013HPCSsaoc/petrenko2013HPCSsaoc_poster.pdf},
	author = {Art Petrenko and Tristan van Leeuwen and Felix J. Herrmann}
}
