Dr. Bas Peters

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Research Scientist at Earth Dynamics AI

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Bas Peters

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Hi! I am a research scientist at Earth Dynamics AI. Before, I was a research scientist at Computational Geosciences Inc. and at Proteic Bioscience (currently DiaGen Ai) in Vancouver BC. Previously, I was a visiting assistant professor (2020-2021) in the mathematics department at Emory University. Before that, I worked for Computational Geosciences Inc. and I was a graduate student in the SLIM group at the University of British Columbia (currently at Georgia Tech).

I have published in applied mathematics, machine learning, and geoscience journals (Journal of Mathematical Imaging and Vision, Research in the Mathematical Sciences, Journal of Applied and Numerical Optimization, Machine Learning Science and Technology, Artificial Intelligence in Geosciences, Journal of Open Source Software, Geophysics, The Leading Edge, Interpretation), in the Handbook of Numerical Analysis, and in the proceedings of SEG, EAGE, EAGE Near Surface Geoscience, ASEG, and an ICLR workshop.

I have presented at SIAM (Annual Meeting, Optimization, Computational Science and Engineering, Mathematical and Computational Issues in the Geosciences), SEG (Annual Meeting, Critical Minerals Forum), EAGE (Annual Conference, Near Surface Geoscience), CVPR and ICLR workshops, Mechanistic Machine Learning and Digital Twins, Machine Learning in Solid Earth Geoscience (Los Alamos), Applied Inverse Problems, the International Conference on Preconditioning Techniques, and the Georgia Scientific Computing Symposium.

My research interests include

Teaching

Emory University:

Fall 2020: Linear Algebra MATH221 (all class info on Canvas)

Spring 2021: Linear Algebra MATH221 (all class info on Canvas)

Recent Publications

Please see my scholar page. for other publications.

Recent & Upcoming Presentations

Deep learning and generative modeling for inverse problems

We develop learned approaches to inverse problems. Paired autoencoders learn low-dimensional latent representations of both the model (parameter) space and the data space, together with mappings between the two latent spaces. This provides surrogate forward and inverse maps that can be trained without access to the likelihood. Related work includes invertible networks and normalizing flows for generative modeling, and machine-learning-based inversion of airborne electromagnetic data.

Seismic inversion with a paired autoencoder. Top: true velocity model and the network prediction. Bottom: inversion in the latent space, initialized with the network prediction, versus conventional inversion from a basic starting model.

Variational paired autoencoders allow sampling, which provides uncertainty estimates: the mean and standard deviation of the samples, and the error of the mean.

Computational methods for training neural networks for large scale inputs

Research focusses on developing fully reversible and invertible networks that have constant memory requirements as a function of network depth. This topic also includes methods for training networks in a ‘factorized’ form to reduce the memory required for weights.

Applications include video segmentation, (time-lapse) hyperspectral land use classification and generative modeling. The low memory requirements of the fully reversible network allows us to segment a full video in one go. The following example segments a full video, based on three given slices.

deep learning for computer vision applications in the geosciences and remote sensing

For this project we develop deep learning methods to be able to apply deep neural-networks to geoscience problems. We worked on techniques to deal with

Applications include aquifer mapping using topography, gravitational, magnetic data, as well as various geological maps and point observations of the ground truth.

Shortcutting inversion-based near-surface characterization workflows using deep learning

Time-lapse hyperspectral imaging maps a 4D input to a 2D maps of the suface of the earth, in terms of land-use change.

2D/3D geological model building from seismic images and borehole data (labels)

Automatic Classification of Geologic Units in Seismic Images Using Partially Interpreted Examples / arXiv

Neural-networks for geophysicists and their application to seismic data interpretation / arXiv

Does shallow geological knowledge help neural-networks to predict deep units? / arXiv

Detecting horizons (interfaces) of interest in seismic images. There are a number of training images and each has a few labels (seed points). Our method performs better than methods not based on learning, especially in areas where there are large gaps in the labels.

Multiresolution neural networks for tracking seismic horizons from few training images / arXiv

Mineral exploration and airborne geophysics: prospectivity mapping, lithology prediction, and processing of airborne data, in collaboration with Computational Geosciences Inc.

Constrained optimization for regularizing inverse problems & neural networks

We incorporate prior knowledge into the inverse problems via a projection of a vector onto an intersection of multiple convex and non-convex sets. Each sets may include a different linear operator, such as discrete derivative matrices, Fourier/DCT/wavelet/curvelet transforms. The projection approach has the advantage that each sets is defined independently of all others; no trade-off/balancing parameters are required. Julia software is available as the SetIntersectionProjection package. Applications include image/video processing and non-convex geophysical parameter estimation problems.

Reconstructing images from noisy, blurred, and missing pixels. Shows basis-pursuit denoise using wavelets, versus our method (PARSDMM): projection onto an intersection of constraint sets that were learned from examples.

In case it is difficult to describe a model/image using a set or intersection of sets as above, we can use an additive model. Therefore, we introduced a generalization of the Minkowski set, which allows us to construct a ‘complicated’ model/image from two ‘simple’ ones. We can add multiple pieces of prior knowledge about each component as well multiple constraints on their sum. In spirit, this approach generalized ideas from cartoon-texture decomposition, robust prinipal component analysis, and morphological component analysis. Julia software is available to set up constraints sets and compute the projection onto the Generalized Minkowski Set.

Generalized Minkowski sets for the regularization of inverse problems (preprint)

Intersections and sums of sets for the regularization of inverse problems (PhD thesis)

The same ideas carry over to neural networks. Constraints on the output, or on the intermediate states, of a network let us include prior knowledge and train from very few labels, without balancing penalty parameters.

Software

SetIntersectionProjection

Generalized Minkowski Set projections

InvertibleNetworks.jl (contributor)

Numerical linear algebra and PDE-constrained optimization

We investigated how and when quadratic penalty methods offer andvantages over reduced-Lagrangian (adjoint-state) methods for non-convex seismic PDE-constrained optimization problems, in terms of the quality of the solution.

Starting from a poor initial model and without data below 7 Hz, wavefield-reconstruction inversion (a penalty method) recovers the main structures, while the reduced-Lagrangian (adjoint-state) method gets stuck.

We also did some work in numerical linear algebra, aimed at seismic parameter estimation problems. We developed a sparse hessian approximation for quadratic-penalty method sub-problems that arise from estimating two different physical parameters simultaneously. This leads to challenges because different physical parameters can have scalings that are orders of magnitudes apart.

A sparse reduced Hessian approximation for multi-parameter wavefield reconstruction inversion/preprint

I developed a solver for block-structured least-squares problems, with slightly more rows than columns. These problems arise when solving for the states/fields when reduced quadratic-penalty methods are employed for time-harmonic PDE-constrained optimization problems. This is the first work that solves such problems in 3D and is based on a identity+low-rank factorization & Sherman-Morrison-Woodbury.

3D acoustic wavefield-reconstruction inversion using this solver: true model (top) and the model estimated with bound constraints (bottom). Yellow circles are sources, purple crosses are receivers.

A numerical solver for least-squares sub-problems in 3D wavefield reconstruction inversion and related problem formulations/preprint

An algorithm for solving least-squares problems with a Helmholtz block and multiple right-hand-sides/slides

Parallel reformulation of the sequential adjoint-state method/preprint