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Combining Benders’ decomposition and parallelisation to solve large-scale adaptive network supply chain management problems
No full textIntegrated supply chain network design—combining warehouse clustering
with inter- and intra-cluster vehicle routing—is a fundamental
feature of supply chain management problems. In this paper, a
Benders’ decomposition-based parallel heuristic approach for the integrated
long-haul and local vehicle routing problem is proposed. The
proposed algorithm comprises lower- and upper-bound search algorithms
running in parallel to find high-quality solutions for challenging
supply chain management problems. A novel Benders’ decomposition
approach is proposed to aid the improvement in the lower bound for
large-scale problems. The results demonstrate that the Benders’ decomposition
approach is effective in finding strong lower bounds and
is beneficial for obtaining high-quality solutions
Improved sampling via learned diffusions
No full textRecently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schrödinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches
Analyzing multimodal probability measures with autoencoders
No full textFinding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively used to complement and possibly bypass expert knowledge in order to construct collective variables. Our focus here is on neural network approaches based on autoencoders. We study some relevant mathematical properties of the loss function considered for training autoencoders, and provide physical interpretations based on conditional variances and minimum energy paths. We also consider various extensions in order to better describe physical systems, by incorporating more information on transition states at saddle points, and/or allowing for multiple decoders in order to describe several transition paths. Our results are illustrated on toy two dimensional systems and on alanine dipeptide
Machine Learning-based Assessment of Multiple Anatomical Structures in Medical Image Data for Diagnosis and Prediction of Knee Osteoarthritis
No full textKnee osteoarthritis (KOA) is a degenerative disease that leads to pain and loss of function. It is estimated to affect over 500 million humans world-wide and is one of the most common reasons for disability. KOA is usually diagnosed by radiologists or clinical experts by anamnesis, physical examination, and by assessing medical image data. The latter is typically acquired using X-Ray or magnetic resonance imaging. Since manual image reading is subjective, tedious and time-consuming, automated methods are required for a fast and objective decision support and for a better understanding of the pathogenesis of KOA.
This thesis sets a foundation towards automated computation of image-based KOA biomarkers for holistic assessment of the knee. This involves the assessment of multiple knee bones and soft tissues. An assessment of particular structures requires localization of these tissues. In order to automate a faithful localization of anatomical structures, deep learning-based methods are investigated and utilized. Additionally, convolutional neural networks (CNNs) are used for classification of medical image data, i.e., for a direct determination of the disease status and to detect anatomical structures and landmarks. The automatically computed anatomical volumes, locations, and other measurements are finally compared to values acquired by clinical experts and evaluated for clustering of KOA groups, classification of KOA severity, prediction of KOA progression, and prediction of total knee replacement.
In various experiments it is shown that CNN-based methods are suitable for accurate medical image segmentation, object detection, landmark detection, and direct classification of disease stages from the image data. Computed features related to the menisci are found to be most expressive in terms of clustering of KOA groups and
predicting of future disease states, thus allowing diagnosis of current KOA conditions and prediction of future conditions.
The conclusion of this thesis is that machine learning-based, fully automated processing of medical image data shows potential for diagnosis and prediction of KOA grades. Future studies could investigate additional features in order to achieve an assessment of the whole knee or validate the findings of this work in clinical
studies
Learning continuous shape priors from sparse data with neural implicit functions
No full textStatistical shape models are an essential tool for various tasks in medical image analysis, including shape generation, reconstruction and classification. Shape models are learned from a population of example shapes, which are typically obtained through segmentation of volumetric medical images. In clinical practice, highly anisotropic volumetric scans with large slice distances are prevalent, e.g., to reduce radiation exposure in CT or image acquisition time in MR imaging. For existing shape modeling approaches, the resolution of the emerging model is limited to the resolution of the training shapes. Therefore, any missing information between slices prohibits existing methods from learning a high-resolution shape prior. We propose a novel shape modeling approach that can be trained on sparse, binary segmentation masks with large slice distances. This is achieved through employing continuous shape representations based on neural implicit functions. After training, our model can reconstruct shapes from various sparse inputs at high target resolutions beyond the resolution of individual training examples. We successfully reconstruct high-resolution shapes from as few as three orthogonal slices. Furthermore, our shape model allows us to embed various sparse segmentation masks into a common, low-dimensional latent space — independent of the acquisition direction, resolution, spacing, and field of view. We show that the emerging latent representation discriminates between healthy and pathological shapes, even when provided with sparse segmentation masks. Lastly, we qualitatively demonstrate that the emerging latent space is smooth and captures characteristic modes of shape variation. We evaluate our shape model on two anatomical structures: the lumbar vertebra and the distal femur, both from publicly available datasets
Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes
No full textLearning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN
No full textThe dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude
Multilevel Optimization for Policy Design with Agent-Based Epidemic Models
No full textEpidemiological models can not only be used to forecast the course of a pandemic like COVID-19, but also to propose and design non-pharmaceutical interventions such as school and work closing. In general, the design of optimal policies leads to nonlinear optimization problems that can be solved by numerical algorithms. Epidemiological models come in different complexities, ranging from systems of simple ordinary differential equations (ODEs) to complex agent-based models (ABMs). The former allow a fast and straightforward optimization, but are limited in accuracy, detail, and parameterization, while the latter can resolve spreading processes in detail, but are extremely expensive to optimize. We consider policy optimization in a prototypical situation modeled as both ODE and ABM, review numerical optimization approaches, and propose a heterogeneous multilevel approach based on combining a fine-resolution ABM and a coarse ODE model. Numerical experiments, in particular with respect to convergence speed, are given for illustrative examples