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Eldad Haber

Eldad Haber appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Machine LearningComputer Visionphysics.geo-phComputational Engineering, Finance, and Sciencemath.OCeess.IVmath.NANumerical AnalysisBiomoleculesDiscrete MathematicsEmerging TechnologiesMathematical Softwarephysics.comp-phquant-ph

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Published work

19 published item(s)

preprint2026arXiv

Conservative Flows: A New Paradigm of Generative Models

Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized from data-supported states rather than from noise. The framework can utilize any pretrained flow model. We develop two probability-preserving sampling mechanisms, a corrected Langevin dynamics with a Metropolis adjustment and a predictor-corrector flow, that operate directly on existing checkpoints. We validate the framework on a synthetic Swiss-roll target, ImageNet-256 and Oxford Flowers-102, where our samplers consistently improve over the original generation procedures.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Target-Aware Data Augmentation for SAT Prediction

Learning-based approaches to NP-hard problems have shown increasing promise, but their progress is fundamentally constrained by the high cost of generating labeled training data. In domains such as Boolean satisfiability (SAT), standard pipelines rely on solver-in-the-loop labeling, which scales poorly with problem size and limits the amount of usable supervision. This bottleneck hinders the broader goal of leveraging machine learning to capture structure in hard combinatorial problems. In this work, we propose a target-aware, solver-free data generation framework for SAT that produces correctly labeled SAT and UNSAT instances by construction, eliminating the need for expensive solver calls. Our method aligns generated instances with the structural properties of a target benchmark, making synthetic data effective for downstream learning. We further develop a linear-programming-aware graph neural network (LPGNN) architecture that incorporates constraint-violation residuals into message passing, enabling the model to exploit underlying optimization structure. Together, these contributions support a data-centric paradigm for learning on NP-hard problems, where scalable, task-aligned data generation is as critical as model design. Our approach yields orders-of-magnitude speedups in data generation, demonstrating that benchmark-aligned synthetic data can effectively augment solver-labeled datasets for GNN-based SAT prediction.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

pathGCN: Learning General Graph Spatial Operators from Paths

Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs. Furthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Mimetic Neural Networks: A unified framework for Protein Design and Folding

Recent advancements in machine learning techniques for protein folding motivate better results in its inverse problem -- protein design. In this work we introduce a new graph mimetic neural network, MimNet, and show that it is possible to build a reversible architecture that solves the structure and design problems in tandem, allowing to improve protein design when the structure is better estimated. We use the ProteinNet data set and show that the state of the art results in protein design can be improved, given recent architectures for protein folding.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Secant Penalized BFGS: A Noise Robust Quasi-Newton Method Via Penalizing The Secant Condition

In this paper, we introduce a new variant of the BFGS method designed to perform well when gradient measurements are corrupted by noise. We show that by treating the secant condition with a penalty method approach motivated by regularized least squares estimation, one can smoothly interpolate between updating the inverse Hessian approximation with the original BFGS update formula and not updating the inverse Hessian approximation. Furthermore, we find the curvature condition is smoothly relaxed as the interpolation moves towards not updating the inverse Hessian approximation, disappearing entirely when the inverse Hessian approximation is not updated. These developments allow us to develop a method we refer to as secant penalized BFGS (SP-BFGS) that allows one to relax the secant condition based on the amount of noise in the gradient measurements. SP-BFGS provides a means of incrementally updating the new inverse Hessian approximation with a controlled amount of bias towards the previous inverse Hessian approximation, which allows one to replace the overwriting nature of the original BFGS update with an averaging nature that resists the destructive effects of noise and can cope with negative curvature measurements. We discuss the theoretical properties of SP-BFGS, including convergence when minimizing strongly convex functions in the presence of uniformly bounded noise. Finally, we present extensive numerical experiments using over 30 problems from the CUTEst test problem set that demonstrate the superior performance of SP-BFGS compared to BFGS in the presence of both noisy function and gradient evaluations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Fully Hyperbolic Convolutional Neural Networks

Convolutional Neural Networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation or 3D medical imaging, has been limited by various factors. Primarily, in the training stage, it is necessary to store network activations for back propagation. In these settings, the memory requirements associated with storing activations can exceed what is feasible with current hardware, especially for problems in 3D. Motivated by the propagation of signals over physical networks, that are governed by the hyperbolic Telegraph equation, in this work we introduce a fully conservative hyperbolic network for problems with high dimensional input and output. We introduce a coarsening operation that allows completely reversible CNNs by using a learnable Discrete Wavelet Transform and its inverse to both coarsen and interpolate the network state and change the number of channels. We show that fully reversible networks are able to achieve results comparable to the state of the art in 4D time-lapse hyper spectral image segmentation and full 3D video segmentation, with a much lower memory footprint that is a constant independent of the network depth. We also extend the use of such networks to Variational Auto Encoders with high resolution input and output.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Fully reversible neural networks for large-scale 3D seismic horizon tracking

Tracking a horizon in seismic images or 3D volumes is an integral part of seismic interpretation. The last few decades saw progress in using neural networks for this task, starting from shallow networks for 1D traces, to deeper convolutional neural networks for large 2D images. Because geological structures are intrinsically 3D, we hope to see improved horizon tracking by training networks on 3D seismic data cubes. While there are some 3D convolutional neural networks for various seismic interpretation tasks, they are restricted to shallow networks or relatively small 3D inputs because of memory limitations. The required memory for the network states and weights increases with network depth. We present a fully reversible network for horizon tracking that has a memory requirement that is independent of network depth. To tackle memory issues regarding the network weights, we use layers that train in a factorized form directly. Therefore, we can maintain a large number of network channels while keeping the number of convolutional kernels low. We use the saved memory to increase the input size of the data by order of magnitude such that the network can better learn from large structures in the data. A field data example verifies the proposed network structure is suitable for seismic horizon tracking.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Fully reversible neural networks for large-scale surface and sub-surface characterization via remote sensing

The large spatial/frequency scale of hyperspectral and airborne magnetic and gravitational data causes memory issues when using convolutional neural networks for (sub-) surface characterization. Recently developed fully reversible networks can mostly avoid memory limitations by virtue of having a low and fixed memory requirement for storing network states, as opposed to the typical linear memory growth with depth. Fully reversible networks enable the training of deep neural networks that take in entire data volumes, and create semantic segmentations in one go. This approach avoids the need to work in small patches or map a data patch to the class of just the central pixel. The cross-entropy loss function requires small modifications to work in conjunction with a fully reversible network and learn from sparsely sampled labels without ever seeing fully labeled ground truth. We show examples from land-use change detection from hyperspectral time-lapse data, and regional aquifer mapping from airborne geophysical and geological data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

LeanConvNets: Low-cost Yet Effective Convolutional Neural Networks

Convolutional Neural Networks (CNNs) have become indispensable for solving machine learning tasks in speech recognition, computer vision, and other areas that involve high-dimensional data. A CNN filters the input feature using a network containing spatial convolution operators with compactly supported stencils. In practice, the input data and the hidden features consist of a large number of channels, which in most CNNs are fully coupled by the convolution operators. This coupling leads to immense computational cost in the training and prediction phase. In this paper, we introduce LeanConvNets that are derived by sparsifying fully-coupled operators in existing CNNs. Our goal is to improve the efficiency of CNNs by reducing the number of weights, floating point operations and latency times, with minimal loss of accuracy. Our lean convolution operators involve tuning parameters that controls the trade-off between the network's accuracy and computational costs. These convolutions can be used in a wide range of existing networks, and we exemplify their use in residual networks (ResNets). Using a range of benchmark problems from image classification and semantic segmentation, we demonstrate that the resulting LeanConvNet's accuracy is close to state-of-the-art networks while being computationally less expensive. In our tests, the lean versions of ResNet in most cases outperform comparable reduced architectures such as MobileNets and ShuffleNets.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Segmentation of Pulmonary Opacification in Chest CT Scans of COVID-19 Patients

The Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has rapidly spread into a global pandemic. A form of pneumonia, presenting as opacities with in a patient's lungs, is the most common presentation associated with this virus, and great attention has gone into how these changes relate to patient morbidity and mortality. In this work we provide open source models for the segmentation of patterns of pulmonary opacification on chest Computed Tomography (CT) scans which have been correlated with various stages and severities of infection. We have collected 663 chest CT scans of COVID-19 patients from healthcare centers around the world, and created pixel wise segmentation labels for nearly 25,000 slices that segment 6 different patterns of pulmonary opacification. We provide open source implementations and pre-trained weights for multiple segmentation models trained on our dataset. Our best model achieves an opacity Intersection-Over-Union score of 0.76 on our test set, demonstrates successful domain adaptation, and predicts the volume of opacification within 1.7\% of expert radiologists. Additionally, we present an analysis of the inter-observer variability inherent to this task, and propose methods for appropriate probabilistic approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2017arXiv

A numerical method for efficient 3D inversions using Richards equation

Fluid flow in the vadose zone is governed by Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Saturation or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysics are being used to supply more spatially and temporally dense data sets. Inferring hydraulic parameters from such datasets requires the ability to efficiently solve and deterministically optimize the nonlinear time domain Richards equation. This is particularly important as the number of parameters to be estimated in a vadose zone inversion continues to grow. In this paper, we describe an efficient technique to invert for distributed hydraulic properties in 1D, 2D, and 3D. Our algorithm does not store the Jacobian, but rather computes the product with a vector, which allows the size of the inversion problem to become much larger than methods such as finite difference or automatic differentiation; which are constrained by computation and memory, respectively. We show our algorithm in practice for a 3D inversion of saturated hydraulic conductivity using saturation data through time. The code to run our examples is open source and the algorithm presented allows this inversion process to run on modest computational resources.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A fast marching algorithm for the factored eikonal equation

The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM) methods. However, when used for a point source, the original eikonal equation is known to yield inaccurate numerical solutions, because of a singularity at the source. In this case, the factored eikonal equation is often preferred, and is known to yield a more accurate numerical solution. One application that requires the solution of the eikonal equation for point sources is travel time tomography. This inverse problem may be formulated using the eikonal equation as a forward problem. While this problem has been solved using FS in the past, the more recent choice for applying it involves FM methods because of the efficiency in which sensitivities can be obtained using them. However, while several FS methods are available for solving the factored equation, the FM method is available only for the original eikonal equation. In this paper we develop a Fast Marching algorithm for the factored eikonal equation, using both first and second order finite-difference schemes. Our algorithm follows the same lines as the original FM algorithm and requires the same computational effort. In addition, we show how to obtain sensitivities using this FM method and apply travel time tomography, formulated as an inverse factored eikonal equation. Numerical results in two and three dimensions show that our algorithm solves the factored eikonal equation efficiently, and demonstrate the achieved accuracy for computing the travel time. We also demonstrate a recovery of a 2D and 3D heterogeneous medium by travel time tomography using the eikonal equation for forward modelling and inversion by Gauss-Newton.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A Framework for the Upscaling of the Electrical Conductivity in the Quasi-static Maxwell's Equations

Electromagnetic simulations of complex geologic settings are computationally expensive. One reason for this is the fact that a fine mesh is required to accurately discretize the electrical conductivity model of a given setting. This conductivity model may vary over several orders of magnitude and these variations can occur over a large range of length scales. Using a very fine mesh for the discretization of this setting leads to the necessity to solve a large system of equations that is often difficult to deal with. To keep the simulations computationally tractable, coarse meshes are often employed for the discretization of the model. Such coarse meshes typically fail to capture the fine-scale variations in the conductivity model resulting in inaccuracies in the predicted data. In this work, we introduce a framework for constructing a coarse-mesh or upscaled conductivity model based on a prescribed fine-mesh model. Rather than using analytical expressions, we opt to pose upscaling as a parameter estimation problem. By solving an optimization problem, we obtain a coarse-mesh conductivity model. The optimization criterion can be tailored to the survey setting in order to produce coarse models that accurately reproduce the predicted data generated on the fine mesh. This allows us to upscale arbitrary conductivity structures, as well as to better understand the meaning of the upscaled quantity. We use 1D and 3D examples to demonstrate that the proposed framework is able to emulate the behavior of the heterogeneity in the fine-mesh conductivity model, and to produce an accurate description of the desired predicted data obtained by using a coarse mesh in the simulation process.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

An oversampling technique for the multiscale finite volume method to simulate electromagnetic responses in the frequency domain

In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static Maxwell's equations in the frequency domain. We assume a coarse mesh nested within a fine mesh that accurately discretizes the problem. For each coarse cell, we independently solve a local version of the original Maxwell's system subject to linear boundary conditions on an extended domain, which includes the coarse cell and a neighborhood of fine cells around it. The local Maxwell's system is solved using the fine mesh contained in the extended domain and the mimetic finite volume method. Next, these local solutions (basis functions) together with a weak-continuity condition are used to construct a coarse-mesh version of the global problem. The basis functions can be used to obtain the fine-mesh details from the solution of the coarse-mesh problem. Our approach leads to a significant reduction in the size of the final system of equations and the computational time, while accurately approximating the behavior of the fine-mesh solutions. We demonstrate the performance of our method using a synthetic 3D example of a mineral deposit.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

jInv -- a flexible Julia package for PDE parameter estimation

Estimating parameters of Partial Differential Equations (PDEs) from noisy and indirect measurements often requires solving ill-posed inverse problems. These so called parameter estimation or inverse medium problems arise in a variety of applications such as geophysical, medical imaging, and nondestructive testing. Their solution is computationally intense since the underlying PDEs need to be solved numerous times until the reconstruction of the parameters is sufficiently accurate. Typically, the computational demand grows significantly when more measurements are available, which poses severe challenges to inversion algorithms as measurement devices become more powerful. In this paper we present jInv, a flexible framework and open source software that provides parallel algorithms for solving parameter estimation problems with many measurements. Being written in the expressive programming language Julia, jInv is portable, easy to understand and extend, cross-platform tested, and well-documented. It provides novel parallelization schemes that exploit the inherent structure of many parameter estimation problems and can be used to solve multiphysics inversion problems as is demonstrated using numerical experiments motivated by geophysical imaging.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Numerical Computation of the Gradient and the Action of the Hessian for Time-Dependent PDE-Constrained Optimization Problems

We present a systematic derivation of the algorithms required for computing the gradient and the action of the Hessian of an arbitrary misfit function for large-scale parameter estimation problems involving linear time-dependent PDEs with stationary coefficients. These algorithms are derived using the adjoint method for time-stepping schemes of arbitrary order and are therefore well-suited for distributed parameter estimation problems where the forward solution needs to be solved to high accuracy. Two examples demonstrate how specific PDEs can be prepared for use with these algorithms. A numerical example illustrates that the order of accuracy of higher-order time-stepping schemes is inherited by their corresponding adjoint time-stepping schemes and misfit gradient computations.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

The Discrete Adjoint Method for Exponential Integration

The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE system is solved using an exponential integrator. We also discuss the closely related topic of computing the action of the sensitivity matrix on a vector, which is required when performing a sensitivity analysis. The PDE system is assumed to be semi-linear and can be the result of a linearization of a nonlinear PDE, leading to exponential Rosenbrock-type methods. We discuss the computation of the derivatives of the $φ$-functions that are used by ETD schemes and find that the derivatives strongly depend on the way the $φ$-functions are evaluated numerically. A general adjoint exponential integration method, required when computing the gradients, is developed and its implementation is illustrated by applying it to the Krogstad scheme. The applicability of the methods developed here to pattern formation problems is demonstrated using the Swift-Hohenberg model.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Building an iterative heuristic solver for a quantum annealer

A quantum annealer heuristically minimizes quadratic unconstrained binary optimization (QUBO) problems, but is limited by the physical hardware in the size and density of the problems it can handle. We have developed a meta-heuristic solver that utilizes D-Wave Systems' quantum annealer (or any other QUBO problem optimizer) to solve larger or denser problems, by iteratively solving subproblems, while keeping the rest of the variables fixed. We present our algorithm, several variants, and the results for the optimization of standard QUBO problem instances from OR-Library of sizes 500 and 2500 as well as the Palubeckis instances of sizes 3000 to 7000. For practical use of the solver, we show the dependence of the time to best solution on the desired gap to the best known solution. In addition, we study the dependence of the gap and the time to best solution on the size of the problems solved by the underlying optimizer.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Simultaneous Source for non-uniform data variance and missing data

The use of simultaneous sources in geophysical inverse problems has revolutionized the ability to deal with large scale data sets that are obtained from multiple source experiments. However, the technique breaks when the data has non-uniform standard deviation or when some data are missing. In this paper we develop, study, and compare a number of techniques that enable to utilize advantages of the simultaneous source framework for these cases. We show that the inverse problem can still be solved efficiently by using these new techniques. We demonstrate our new approaches on the Direct Current Resistivity inverse problem.

0 citations0 reviewsNo code linkedOpen access