508 research outputs found

    A Methodology to Enable Concurrent Trade Space Exploration of Space Campaigns and Transportation Systems

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    Space exploration campaigns detail the ways and means to achieve goals for our human spaceflight programs. Significant strategic, financial, and programmatic investments over long timescales are required to execute them, and therefore must be justified to decision makers. To make an informed down-selection, many alternative campaign designs are presented at the conceptual-level, as a set and sequence of individual missions to perform that meets the goals and constraints of the campaign, either technical or programmatic. Each mission is executed by in-space transportation systems, which deliver either crew or cargo payloads to various destinations. Design of each of these transportation systems is highly dependent on campaign goals and even small changes in subsystem design parameters can prompt significant changes in the overall campaign strategy. However, the current state of the art describes campaign and vehicle design processes that are generally performed independently, which limits the ability to assess these sensitive impacts. The objective of this research is to establish a methodology for space exploration campaign design that represents transportation systems as a collection of subsystems and integrates its design process to enable concurrent trade space exploration. More specifically, the goal is to identify existing campaign and vehicle design processes to use as a foundation for improvement and eventual integration. In the past two decades, researchers have adopted terrestrial logistics and supply chain optimization processes to the space campaign design problem by accounting for the challenges that accompany space travel. Fundamentally, a space campaign is formulated as a network design problem where destinations, such as orbits or surfaces of planetary bodies, are represented as nodes with the routes between them as arcs. The objective of this design problem is to optimize the flow of commodities within network using available transport systems. Given the dynamic nature and the number of commodities involved, each campaign can be modeled as a time-expanded, generalized multi-commodity network flow and solved using a mixed integer programming algorithm. To address the challenge of modeling complex concept of operations (ConOps), this formulation was extended to include paths as a set of arcs, further enabling the inclusion of vehicle stacks and payload transfers in the campaign optimization process. Further, with the focus of transportation system within this research, the typical fixed orbital nodes in the logistics network are modified to represent ranges of orbits, categorized by their characteristic energy. This enables the vehicle design process to vary each orbit in the mission as it desires to find the best one per vehicle. By extension, once integrated, arc costs of dV and dT are updated each iteration. Once campaign goals and external constraints are included, the formulated campaign design process generates alternatives at the conceptual level, where each one identifies the optimal set and sequence of missions to perform. Representing transportation systems as a collection of subsystems introduces challenges in the design of each vehicle, with a high degree of coupling between each subsystem as well as the driving mission. Additionally, sizing of each subsystem can have many inputs and outputs linked across the system, resulting in a complex, multi-disciplinary analysis, and optimization problem. By leveraging the ontology within the Dynamic Rocket Equation Tool, DYREQT, this problem can be solved rapidly by defining each system as a hierarchy of elements and subelements, the latter corresponding to external subsystem-level sizing models. DYREQT also enables the construction of individual missions as a series of events, which can be directly driven and generated by the mission set found by the campaign optimization process. This process produces sized vehicles iteratively by using the mission input, subsystem level sizing models, and the ideal rocket equation. By conducting a literature review of campaign and vehicle design processes, the different pieces of the overall methodology are identified, but not the structure. The specific iterative solver, the corresponding convergence criteria, and initialization scheme are the primary areas for experimentation of this thesis. Using NASA’s reference 3-element Human Landing System campaign, the results of these experiments show that the methodology performs best with the vehicle sizing and synthesis process initializing and a path guess that minimizes dV. Further, a converged solution is found faster using non-linear Gauss Seidel fixed point iteration over Jacobi and set of convergence criteria that covers vehicle masses and mission data. To show improvement over the state of the art, and how it enables concurrent trade studies, this methodology is used at scale in a demonstration using NASA’s Design Reference Architecture 5.0. The LH2 Nuclear Thermal Propulsion (NTP) option is traded with NH3and H2O at the vehicle-level as a way to show the impacts of alternative propellants on the vehicle sizing and campaign strategy. Martian surface stay duration is traded at the campaign-level through two options: long-stay and short-stay. The methodology was able to produce four alternative campaigns over the course of two weeks, which provided data about the launch and aggregation strategy, mission profiles, high-level figures of merit, and subsystem-level vehicle sizes for each alternative. Expectedly, with their lower specific impulses, alternative NTP propellants showed significant growth in the overall mass required to execute each campaign, subsequently represented the number of drop tanks and launches. Further, the short-stay campaign option showed a similar overall mass required compared to its long-stay counterpart, but higher overall costs even given the fewer elements required. Both trade studies supported the overall hypothesis and that integrating the campaign and vehicle design processes addresses the coupling between then and directly shows the impacts of their sensitivities on each other. As a result, the research objective was fulfilled by producing a methodology that was able to address the key gaps identified in the current state of the art.Ph.D

    OCDaf: Ordered Causal Discovery with Autoregressive Flows

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    We propose OCDaf, a novel order-based method for learning causal graphs from observational data. We establish the identifiability of causal graphs within multivariate heteroscedastic noise models, a generalization of additive noise models that allow for non-constant noise variances. Drawing upon the structural similarities between these models and affine autoregressive normalizing flows, we introduce a continuous search algorithm to find causal structures. Our experiments demonstrate state-of-the-art performance across the Sachs and SynTReN benchmarks in Structural Hamming Distance (SHD) and Structural Intervention Distance (SID). Furthermore, we validate our identifiability theory across various parametric and nonparametric synthetic datasets and showcase superior performance compared to existing baselines

    Anwendungen maschinellen Lernens fĂŒr datengetriebene PrĂ€vention auf Populationsebene

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    Healthcare costs are systematically rising, and current therapy-focused healthcare systems are not sustainable in the long run. While disease prevention is a viable instrument for reducing costs and suffering, it requires risk modeling to stratify populations, identify high- risk individuals and enable personalized interventions. In current clinical practice, however, systematic risk stratification is limited: on the one hand, for the vast majority of endpoints, no risk models exist. On the other hand, available models focus on predicting a single disease at a time, rendering predictor collection burdensome. At the same time, the den- sity of individual patient data is constantly increasing. Especially complex data modalities, such as -omics measurements or images, may contain systemic information on future health trajectories relevant for multiple endpoints simultaneously. However, to date, this data is inaccessible for risk modeling as no dedicated methods exist to extract clinically relevant information. This study built on recent advances in machine learning to investigate the ap- plicability of four distinct data modalities not yet leveraged for risk modeling in primary prevention. For each data modality, a neural network-based survival model was developed to extract predictive information, scrutinize performance gains over commonly collected covariates, and pinpoint potential clinical utility. Notably, the developed methodology was able to integrate polygenic risk scores for cardiovascular prevention, outperforming existing approaches and identifying benefiting subpopulations. Investigating NMR metabolomics, the developed methodology allowed the prediction of future disease onset for many common diseases at once, indicating potential applicability as a drop-in replacement for commonly collected covariates. Extending the methodology to phenome-wide risk modeling, elec- tronic health records were found to be a general source of predictive information with high systemic relevance for thousands of endpoints. Assessing retinal fundus photographs, the developed methodology identified diseases where retinal information most impacted health trajectories. In summary, the results demonstrate the capability of neural survival models to integrate complex data modalities for multi-disease risk modeling in primary prevention and illustrate the tremendous potential of machine learning models to disrupt medical practice toward data-driven prevention at population scale.Die Kosten im Gesundheitswesen steigen systematisch und derzeitige therapieorientierte Gesundheitssysteme sind nicht nachhaltig. Angesichts vieler verhinderbarer Krankheiten stellt die PrĂ€vention ein veritables Instrument zur Verringerung von Kosten und Leiden dar. Risikostratifizierung ist die grundlegende Voraussetzung fĂŒr ein prĂ€ventionszentri- ertes Gesundheitswesen um Personen mit hohem Risiko zu identifizieren und Maßnah- men einzuleiten. Heute ist eine systematische Risikostratifizierung jedoch nur begrenzt möglich, da fĂŒr die meisten Krankheiten keine Risikomodelle existieren und sich verfĂŒg- bare Modelle auf einzelne Krankheiten beschrĂ€nken. Weil fĂŒr deren Berechnung jeweils spezielle Sets an PrĂ€diktoren zu erheben sind werden in Praxis oft nur wenige Modelle angewandt. Gleichzeitig versprechen komplexe DatenmodalitĂ€ten, wie Bilder oder -omics- Messungen, systemische Informationen ĂŒber zukĂŒnftige GesundheitsverlĂ€ufe, mit poten- tieller Relevanz fĂŒr viele Endpunkte gleichzeitig. Da es an dedizierten Methoden zur Ex- traktion klinisch relevanter Informationen fehlt, sind diese Daten jedoch fĂŒr die Risikomod- ellierung unzugĂ€nglich, und ihr Potenzial blieb bislang unbewertet. Diese Studie nutzt ma- chinelles Lernen, um die Anwendbarkeit von vier DatenmodalitĂ€ten in der PrimĂ€rprĂ€ven- tion zu untersuchen: polygene Risikoscores fĂŒr die kardiovaskulĂ€re PrĂ€vention, NMR Meta- bolomicsdaten, elektronische Gesundheitsakten und Netzhautfundusfotos. Pro Datenmodal- itĂ€t wurde ein neuronales Risikomodell entwickelt, um relevante Informationen zu extra- hieren, additive Information gegenĂŒber ĂŒblicherweise erfassten Kovariaten zu quantifizieren und den potenziellen klinischen Nutzen der DatenmodalitĂ€t zu ermitteln. Die entwickelte Me-thodik konnte polygene Risikoscores fĂŒr die kardiovaskulĂ€re PrĂ€vention integrieren. Im Falle der NMR-Metabolomik erschloss die entwickelte Methodik wertvolle Informa- tionen ĂŒber den zukĂŒnftigen Ausbruch von Krankheiten. Unter Einsatz einer phĂ€nomen- weiten Risikomodellierung erwiesen sich elektronische Gesundheitsakten als Quelle prĂ€dik- tiver Information mit hoher systemischer Relevanz. Bei der Analyse von Fundusfotografien der Netzhaut wurden Krankheiten identifiziert fĂŒr deren Vorhersage Netzhautinformationen genutzt werden könnten. Zusammengefasst zeigten die Ergebnisse das Potential neuronaler Risikomodelle die medizinische Praxis in Richtung einer datengesteuerten, prĂ€ventionsori- entierten Medizin zu verĂ€ndern

    Measuring the impact of COVID-19 on hospital care pathways

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    Care pathways in hospitals around the world reported significant disruption during the recent COVID-19 pandemic but measuring the actual impact is more problematic. Process mining can be useful for hospital management to measure the conformance of real-life care to what might be considered normal operations. In this study, we aim to demonstrate that process mining can be used to investigate process changes associated with complex disruptive events. We studied perturbations to accident and emergency (A &E) and maternity pathways in a UK public hospital during the COVID-19 pandemic. Co-incidentally the hospital had implemented a Command Centre approach for patient-flow management affording an opportunity to study both the planned improvement and the disruption due to the pandemic. Our study proposes and demonstrates a method for measuring and investigating the impact of such planned and unplanned disruptions affecting hospital care pathways. We found that during the pandemic, both A &E and maternity pathways had measurable reductions in the mean length of stay and a measurable drop in the percentage of pathways conforming to normative models. There were no distinctive patterns of monthly mean values of length of stay nor conformance throughout the phases of the installation of the hospital’s new Command Centre approach. Due to a deficit in the available A &E data, the findings for A &E pathways could not be interpreted

    Applications of Deep Learning to Differential Equation Models in Oncology

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    The integration of quantitative tools in biology and medicine has led to many groundbreaking advances in recent history, with many more promising discoveries on the horizon. Conventional mathematical models, particularly differential equation-based models, have had great success in various biological applications, including modelling bacterial growth, disease propagation, and tumour spread. However, these approaches can be somewhat limited due to their reliance on known parameter values, initial conditions, and boundary conditions, which can dull their applicability. Furthermore, their forms are directly tied to mechanistic phenomena, making these models highly explainable, but also requiring a comprehensive understanding of the underlying dynamics before modelling the system. On the other hand, machine learning models typically require less prior knowledge of the system but require a significant amount of data for training. Although machine learning models can be more flexible, they tend to be black boxes, making them difficult to interpret. Hybrid models, which combine conventional and machine learning approaches, have the potential to achieve the best of both worlds. These models can provide explainable outcomes while relying on minimal assumptions or data. An example of this is physics-informed neural networks, a novel deep learning approach that incorporates information from partial differential equations into the optimization of a neural network. This hybrid approach offers significant potential in various contexts where differential equation models are known, but data is scarce or challenging to work with. Precision oncology is one such field. This thesis employs hybrid conventional/machine learning models to address problems in cancer medicine, specifically aiming to advance personalized medicine approaches. It contains three projects. In the first, a hybrid approach is used to make patient-specific characterizations of brain tumours using medical imaging data. In the second project, a hybrid approach is employed to create subject-specific projections of drug-carrying cancer nanoparticle accumulation and intratumoral interstitial fluid pressure. In the final project, a hybrid approach is utilized to optimize radiation therapy scheduling for tumours with heterogeneous cell populations and cancer stem cells. Overall, this thesis showcases several examples of how quantitative tools, particularly those involving both conventional and machine learning approaches, can be employed to tackle challenges in oncology. It further supports the notion that the continued integration of quantitative tools in medicine is a key strategy in addressing problems and open questions in healthcare

    Metal Cations in Protein Force Fields: From Data Set Creation and Benchmarks to Polarizable Force Field Implementation and Adjustment

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    Metal cations are essential to life. About one-third of all proteins require metal cofactors to accurately fold or to function. Computer simulations using empirical parameters and classical molecular mechanics models (force fields) are the standard tool to investigate proteins’ structural dynamics and functions in silico. Despite many successes, the accuracy of force fields is limited when cations are involved. The focus of this thesis is the development of tools and strategies to create system-specific force field parameters to accurately describe cation-protein interactions. The accuracy of a force field mainly relies on (i) the parameters derived from increasingly large quantum chemistry or experimental data and (ii) the physics behind the energy formula. The first part of this thesis presents a large and comprehensive quantum chemistry data set on a consistent computational footing that can be used for force field parameterization and benchmarking. The data set covers dipeptides of the 20 proteinogenic amino acids with different possible side chain protonation states, 3 divalent cations (Ca2+, Mg2+, and Ba2+), and a wide relative energy range. Crucial properties related to force field development, such as partial charges, interaction energies, etc., are also provided. To make the data available, the data set was uploaded to the NOMAD repository and its data structure was formalized in an ontology. Besides a proper data basis for parameterization, the physics covered by the terms of the additive force field formulation model impacts its applicability. The second part of this thesis benchmarks three popular non-polarizable force fields and the polarizable Drude model against a quantum chemistry data set. After some adjustments, the Drude model was found to reproduce the reference interaction energy substantially better than the non-polarizable force fields, which showed the importance of explicitly addressing polarization effects. Tweaking of the Drude model involved Boltzmann-weighted fitting to optimize Thole factors and Lennard-Jones parameters. The obtained parameters were validated by (i) their ability to reproduce reference interaction energies and (ii) molecular dynamics simulations of the N-lobe of calmodulin. This work facilitates the improvement of polarizable force fields for cation-protein interactions by quantum chemistry-driven parameterization combined with molecular dynamics simulations in the condensed phase. While the Drude model exhibits its potential simulating cation-protein interactions, it lacks description of charge transfer effects, which are significant between cation and protein. The CTPOL model extends the classical force field formulation by charge transfer (CT) and polarization (POL). Since the CTPOL model is not readily available in any of the popular molecular-dynamics packages, it was implemented in OpenMM. Furthermore, an open-source parameterization tool, called FFAFFURR, was implemented that enables the (system specific) parameterization of OPLS-AA and CTPOL models. Following the method established in the previous part, the performance of FFAFFURR was evaluated by its ability to reproduce quantum chemistry energies and molecular dynamics simulations of the zinc finger protein. In conclusion, this thesis steps towards the development of next-generation force fields to accurately describe cation-protein interactions by providing (i) reference data, (ii) a force field model that includes charge transfer and polarization, and (iii) a freely-available parameterization tool.Metallkationen sind fĂŒr das Leben unerlĂ€sslich. Etwa ein Drittel aller Proteine benötigen Metall-Cofaktoren, um sich korrekt zu falten oder zu funktionieren. Computersimulationen unter Verwendung empirischer Parameter und klassischer MolekĂŒlmechanik-Modelle (Kraftfelder) sind ein Standardwerkzeug zur Untersuchung der strukturellen Dynamik und Funktionen von Proteinen in silico. Trotz vieler Erfolge ist die Genauigkeit der Kraftfelder begrenzt, wenn Kationen beteiligt sind. Der Schwerpunkt dieser Arbeit liegt auf der Entwicklung von Werkzeugen und Strategien zur Erstellung systemspezifischer Kraftfeldparameter zur genaueren Beschreibung von Kationen-Protein-Wechselwirkungen. Die Genauigkeit eines Kraftfelds hĂ€ngt hauptsĂ€chlich von (i) den Parametern ab, die aus immer grĂ¶ĂŸeren quantenchemischen oder experimentellen Daten abgeleitet werden, und (ii) der Physik hinter der Kraftfeld-Formel. Im ersten Teil dieser Arbeit wird ein großer und umfassender quantenchemischer Datensatz auf einer konsistenten rechnerischen Grundlage vorgestellt, der fĂŒr die Parametrisierung und das Benchmarking von Kraftfeldern verwendet werden kann. Der Datensatz umfasst Dipeptide der 20 proteinogenen AminosĂ€uren mit verschiedenen möglichen Seitenketten-ProtonierungszustĂ€nden, 3 zweiwertige Kationen (Ca2+, Mg2+ und Ba2+) und einen breiten relativen Energiebereich. Wichtige Eigenschaften fĂŒr die Entwicklung von Kraftfeldern, wie Wechselwirkungsenergien, Partialladungen usw., werden ebenfalls bereitgestellt. Um die Daten verfĂŒgbar zu machen, wurde der Datensatz in das NOMAD-Repository hochgeladen und seine Datenstruktur wurde in einer Ontologie formalisiert. Neben einer geeigneten Datenbasis fĂŒr die Parametrisierung beeinflusst die Physik, die von den Termen des additiven Kraftfeld-Modells abgedeckt wird, dessen Anwendbarkeit. Der zweite Teil dieser Arbeit vergleicht drei populĂ€re nichtpolarisierbare Kraftfelder und das polarisierbare Drude-Modell mit einem Datensatz aus der Quantenchemie. Nach einigen Anpassungen stellte sich heraus, dass das Drude-Modell die Referenzwechselwirkungsenergie wesentlich besser reproduziert als die nichtpolarisierbaren Kraftfelder, was zeigt, wie wichtig es ist, Polarisationseffekte explizit zu berĂŒcksichtigen. Die Anpassung des Drude-Modells umfasste eine Boltzmann-gewichtete Optimierung der Thole-Faktoren und Lennard-Jones-Parameter. Die erhaltenen Parameter wurden validiert durch (i) ihre FĂ€higkeit, Referenzwechselwirkungsenergien zu reproduzieren und (ii) Molekulardynamik-Simulationen des Calmodulin-N-Lobe. Diese Arbeit demonstriert die Verbesserung polarisierbarer Kraftfelder fĂŒr Kationen-Protein-Wechselwirkungen durch quantenchemisch gesteuerte Parametrisierung in Kombination mit Molekulardynamiksimulationen in der kondensierten Phase. WĂ€hrend das Drude-Modell sein Potenzial bei der Simulation von Kation - Protein - Wechselwirkungen zeigt, fehlt ihm die Beschreibung von Ladungstransfereffekten, die zwischen Kation und Protein von Bedeutung sind. Das CTPOL-Modell erweitert die klassische Kraftfeldformulierung um den Ladungstransfer (CT) und die Polarisation (POL). Da das CTPOL-Modell in keinem der gĂ€ngigen Molekulardynamik-Pakete verfĂŒgbar ist, wurde es in OpenMM implementiert. Außerdem wurde ein Open-Source-Parametrisierungswerkzeug namens FFAFFURR implementiert, welches die (systemspezifische) Parametrisierung von OPLS-AA und CTPOL-Modellen ermöglicht. In Anlehnung an die im vorangegangenen Teil etablierte Methode wurde die Leistung von FFAFFURR anhand seiner FĂ€higkeit, quantenchemische Energien und Molekulardynamiksimulationen des Zinkfingerproteins zu reproduzieren, bewertet. Zusammenfassend lĂ€sst sich sagen, dass diese Arbeit einen Schritt in Richtung der Entwicklung von Kraftfeldern der nĂ€chsten Generation zur genauen Beschreibung von Kationen-Protein-Wechselwirkungen darstellt, indem sie (i) Referenzdaten, (ii) ein Kraftfeldmodell, das Ladungstransfer und Polarisation einschließt, und (iii) ein frei verfĂŒgbares Parametrisierungswerkzeug bereitstellt

    Essays on Identification of Structural VARMA models

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    This research has been possible thanks to the financial support from the scholarship MCIN/BES-2017-081997 from the Spanish Agency of Science and Innovation (Ministerio de Ciencia e Innovación).Programa de Doctorado en Economía por la Universidad Carlos III de MadridPresidente: Juan José Dolado Lobregad.- Secretario: Dante Amengual.- Vocal: Geert Mester

    Robust data driven discovery of a seismic wave equation

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    Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore recently, a branch of machine learning has been devoted to the discovery of physical laws from data. We test such discovery algorithms, with our own flavor of implementation D-WE, in discovering the wave equation from the observed spatial-temporal wavefields. D-WE first pretrains a neural network (NN) in a supervised fashion to establish the mapping between the spatial-temporal locations (x,y,z,t) and the observation displacement wavefield function u(x,y,z,t). The trained NN serves to generate meta-data and provide the time and spatial derivatives of the wavefield (e.g., u_tt and u_xx) by automatic differentiation. Then, a preliminary library of potential terms for the wave equation is optimized from an overcomplete library by using a genetic algorithm. We, then, use a physics-informed information criterion to evaluate the precision and parsimony of potential equations in the preliminary library and determine the best structure of the wave equation. Finally, we train the "physics-informed" neural network to identify the corresponding coefficients of each functional term. Examples in discovering the 2D acoustic wave equation validate the feasibility and effectiveness of D-WE. We also verify the robustness of this method by testing it on noisy and sparsely acquired wavefield data

    Mesoscopic Physics of Quantum Systems and Neural Networks

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    We study three different kinds of mesoscopic systems – in the intermediate region between macroscopic and microscopic scales consisting of many interacting constituents: We consider particle entanglement in one-dimensional chains of interacting fermions. By employing a field theoretical bosonization calculation, we obtain the one-particle entanglement entropy in the ground state and its time evolution after an interaction quantum quench which causes relaxation towards non-equilibrium steady states. By pushing the boundaries of the numerical exact diagonalization and density matrix renormalization group computations, we are able to accurately scale to the thermodynamic limit where we make contact to the analytic field theory model. This allows to fix an interaction cutoff required in the continuum bosonization calculation to account for the short range interaction of the lattice model, such that the bosonization result provides accurate predictions for the one-body reduced density matrix in the Luttinger liquid phase. Establishing a better understanding of how to control entanglement in mesoscopic systems is also crucial for building qubits for a quantum computer. We further study a popular scalable qubit architecture that is based on Majorana zero modes in topological superconductors. The two major challenges with realizing Majorana qubits currently lie in trivial pseudo-Majorana states that mimic signatures of the topological bound states and in strong disorder in the proposed topological hybrid systems that destroys the topological phase. We study coherent transport through interferometers with a Majorana wire embedded into one arm. By combining analytical and numerical considerations, we explain the occurrence of an amplitude maximum as a function of the Zeeman field at the onset of the topological phase – a signature unique to MZMs – which has recently been measured experimentally [Whiticar et al., Nature Communications, 11(1):3212, 2020]. By placing an array of gates in proximity to the nanowire, we made a fruitful connection to the field of Machine Learning by using the CMA-ES algorithm to tune the gate voltages in order to maximize the amplitude of coherent transmission. We find that the algorithm is capable of learning disorder profiles and even to restore Majorana modes that were fully destroyed by strong disorder by optimizing a feasible number of gates. Deep neural networks are another popular machine learning approach which not only has many direct applications to physical systems but which also behaves similarly to physical mesoscopic systems. In order to comprehend the effects of the complex dynamics from the training, we employ Random Matrix Theory (RMT) as a zero-information hypothesis: before training, the weights are randomly initialized and therefore are perfectly described by RMT. After training, we attribute deviations from these predictions to learned information in the weight matrices. Conducting a careful numerical analysis, we verify that the spectra of weight matrices consists of a random bulk and a few important large singular values and corresponding vectors that carry almost all learned information. By further adding label noise to the training data, we find that more singular values in intermediate parts of the spectrum contribute by fitting the randomly labeled images. Based on these observations, we propose a noise filtering algorithm that both removes the singular values storing the noise and reverts the level repulsion of the large singular values due to the random bulk
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