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DOE OSTI2015

On-chip generation of Einstein-Podolsky-Rosen states with arbitrary symmetry

We experimentally demonstrate a method for integrated-optical generation of two-photon Einstein-Podolsky-Rosen states featuring arbitrary symmetries. In our setting, we employ detuned directional couplers to impose a freely tailorable phase between the two modes of the state. Our results allow to mimic the quantum random walk statistics of bosons, fermions, and anyons, particles with fractional exchange statistics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Automated Calibration System for Beam Current Monitor

The Beam Current Monitor (BCM) measures the instantaneous current in a beam. This work aims to develop an automated calibration system for the BCM to address the need for calibration without interrupting beam operation. We strive to create a synchronous calibration method integrated into the master timeline by utilizing the pulsed nature of synchrotrons to run calibration pulses during inter-pulse gaps. This improvement should enhance operational efficiency, ensure safe operation, and help mitigate beam loss, all by enabling intermittent calibration during the operation of the accelerator. This is accomplished by developing a Python program that interfaces with a Keithley 6221 DC and AC source and a Keithley 2182A Nanovoltmeter. The program configures both of these devices to perform a selected mode of the current sweep, allows for the initiation of the current sweep, collects the measured voltage data from the 2182A, stores the collected data to the computer in a CSV file, and graphs the collected data.

Haller, James↗

DOE OSTI2026

Navigating Large Chemical Spaces Using Graph Theory and Integer Programming

Navigating and analyzing large chemical spaces are necessary to accelerate the design and discovery of new molecules and chemical processes. In this work, we introduce a computational framework that integrates graph theory and integer programming to enable the efficient navigation of large chemical spaces. Our framework represents the chemical space as a graph, wherein nodes represent molecules and edges represent the degree of similarity or connectivity based on domain-specific information. Using the graph representation, we identify representative molecules by computing the so-called minimum dominating set (MDS), which in our context is the minimum set of molecules that is connected to all other molecules. We present a suite of solution strategies for the MDS problem including heuristic and rigorous integer programming (IP) approaches. We show that these approaches allow us to capture physicochemical properties and domain-specific logic and constraints, facilitating the identification of molecules with the target properties. We demonstrate the effectiveness of the proposed approach by navigating the chemical space of per- and polyfluoroalkyl substances (PFAS); this comprises approximately 15,000 molecular structures. We compare our framework against traditional dimensionality reduction and clustering methods such as t-SNE and K-means clustering.

Chemical structure↗

DOE OSTI2018

Resource Aware Intelligent Network Services (RAINS) Final Technical Report

The Resource Aware Intelligent Network Services (RAINS) project conducted research and developed technologies in the area of cyber infrastructure resource modeling and computation. The goal of this work was to provide a foundation to enable intelligent, software defined services which spanned the network AND the resources which connect to the network. A Multi-Resource Service Plane (MRSP) was defined, which allows resource owners/managers to locate and place themselves from a topology and service availability perspective within the dynamic networked cyberinfrastructure ecosystem. The MRSP enables the presentation of integrated topology views and computation results which can include resources across the spectrum of compute, storage, and networks. The RAINS project developed MSRP includes the following key components: i) Multi-Resource Service (MRS) Ontology/Multi-Resource Markup Language (MRML), ii) Resource Computation Engine (RCE), iii) Modular Driver Framework (to allow integration of a variety of external resources). The MRS/MRML is a general and extensible modeling framework that allows for resource owners to model, or describe, a wide variety of resource types. All resources are described using three categories of elements: Resources, Services, and Relationships between the elements. This modeling framework defines a common method for the transformation of cyber infrastructure resources into data in the form of MRML models. In order to realize this infrastructure datification, the RAINS project developed a model based computation system, i.e. “RAINS Computation Engine (RCE)”. The RCE has the ability to ingest, process, integrate, and compute based on automatically generated MRML models. The RCE interacts with the resources thru system drivers which are specific to the type of external network or resource controller. The RAINS project developed a modular and pluggable driver system which facilities a variety of resource controllers to automatically generate, maintain, and distribute MRML based resource descriptions. Once all of the resource topologies are absorbed by the RCE, a connected graph of the full distributed system topology is constructed, which forms the basis for computation and workflow processing. The RCE includes a Modular Computation Element (MCE) framework which allows for tailoring of the computation process to the specific set of resources under control, and the services desired. The input and output of an MCE are both model data based on MRS/MRML ontology and schema. Some of the RAINS project accomplishments include: Development of general and extensible multi-resource modeling framework; Design of a Resource Computation Engine (RCE) system which includes the following key capabilities; Absorb a variety of multi-resource model types and build integrated models; Novel architecture which uses model based communications across the full stack for all Flexible provision of abstract or intent based user facing interfaces; Workflow processing based on model descriptions; Release of the RCE as an open source software; Deployment of RCE in the University of Maryland/Mid-Atlantic Crossroad ScienceDMZ in prototype mode with a plan under way to transition to production; Deployment at the Argonne National Laboratory DTN Facility in prototype mode; Selection of RCE by the DOE SENSE (SDN for End-to-end Networked Science at the Exascale) project as the basis for their orchestration service.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

The Number and Pattern of Viral Genomic Reassortments are not Necessarily Identifiable from Segment Trees

Reassortment is an evolutionary process common in viruses with segmented genomes. These viruses can swap whole genomic segments during cellular co-infection, giving rise to novel progeny formed from the mixture of parental segments. Since large-scale genome rearrangements have the potential to generate new phenotypes, reassortment is important to both evolutionary biology and public health research. However, statistical inference of the pattern of reassortment events from phylogenetic data is exceptionally difficult, potentially involving inference of general graphs in which individual segment trees are embedded. In this paper, we argue that, in general, the number and pattern of reassortment events are not identifiable from segment trees alone, even with theoretically ideal data. We call this fact the fundamental problem of reassortment, which we illustrate using the concept of the “first-infection tree,” a potentially counterfactual genealogy that would have been observed in the segment trees had no reassortment occurred. Further, we illustrate four additional problems that can arise logically in the inference of reassortment events and show, using simulated data, that these problems are not rare and can potentially distort our observation of reassortment even in small data sets. Finally, we discuss how existing methods can be augmented or adapted to account for not only the fundamental problem of reassortment, but also the four additional situations that can complicate the inference of reassortment.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

A General Spatiotemporal Imputation Framework for Missing Sensor Data

Many applications from precision agriculture, environmental monitoring and transportation networks rely on data collected across space and time over a large geographic area. Missing data poses a significant challenge for any data-driven inference and control tasks. Data imputation or the estimation of missing data can help fill these gaps by utilizing inherent spatial relationships and temporal patterns. A variety of spatiotemporal imputation models have been developed to address missing data in spatiotemporal datasets. However, these classical methods rely on the assumption that the underlying data follows a smooth trend and fail to provide accurate estimates when there is a large number of missing points in the data. Even though there are machine learning driven tensor completion approaches such as convolutional neural network based tensor completion (CoSTCo) that capture the non-linear relationships in the dataset, the transductive nature makes the algorithm less scalable. Thus, existing approaches for estimating the missing information do not effectively capture all dimensions of the spatiotemporal data structure, resulting in erroneous predictions and poor performance. The main contributions of this paper are: (1) We propose a novel inductive framework (G-LSTM) for missing data imputation that integrates a graph neural network with LSTMs to effectively capture both spatial and temporal dependencies. (2) Experimental results on a traffic dataset demonstrate that the proposed GNN integrated with an LSTM framework achieves improved imputation and maintains steady performance even when there are extreme missing conditions in comparison with the state-of-the-art imputation framework (i.e, CoSTCo). (3) The simulation results on a traffic network show up to 69% reduction in mean absolute error and 61% reduction in root mean square error when compared to CoSTCo.

Tharzeen, Aabila↗

DOE OSTI2024

Efficient Anomaly Detection Driven By Different Machine Learning Architectures And Models

The rapid growth and ubiquitous adoption of the internet and cyber-physical systems (CPS) have fundamentally transformed modern communication, work, and human-system interactions. While networks now form the backbone of critical digital ecosystems, enabling seamless data transmission across diverse, interconnected systems, this increased connectivity also expands the attack surface, making real-time detection of network intrusions and anomalies a pressing challenge. Detecting unusual activities within network infrastructure requires advanced data traffic analysis to differentiate between legitimate and malicious interactions. Traditional approaches to network anomaly detectionâ??such as rule-based and signature-based systemsâ??often depend on predefined patterns to identify known anomalies, limiting their effectiveness against emerging, stealthy, or previously unseen threats. These conventional methods suffer from high false alarm rates and fail to adapt to the ever-evolving nature of network traffic, particularly in large-scale, decentralized environments where data volume, velocity, and variety are constantly increasing. This dissertation presents artificial intelligence (AI)-driven approaches to anomaly detection that leverage graphics processing unit (GPU)-enabled high-performance computing (HPC) platforms for processing massive network traffic data and monitoring the components of cyber-physical systems (CPS) for potentially hazardous conditions. The research advances several key contributions: (1) Designing efficient machine learning techniques for CPS condition monitoring and anomaly detection; (2) enabling federated learning (FL) frameworks that enable distributed detection while preserving data privacy and system resilience; (3) exploring graph-based methodologies combining graph neural networks (GNN) and graph machine learning (ML) approaches for the Internet of Things (IoT) and automotive network security, and (4) performing distributed edge computing optimizations that integrate FL with scalable technologies for reduced communication overhead. Through extensive experiments, these methodologies demonstrate that complex anomaly detection and condition monitoring tasks can be achieved while balancing computational efficiency and detection accuracy through fine-grained network information processing. The frameworks developed in this research establish a robust foundation for network anomaly detection, providing scalable, adaptive, and privacy-preserving solutions for safeguarding CPS and IoT networks in an increasingly interconnected digital landscape. The practical implications of these research findings are significant, as they can inform the development of next-generation network security systems and contribute to the protection of critical infrastructure against sophisticated cyber attacks.

Marfo, William↗

DOE OSTI2014

[{sup 18}F]FDG-PET Standard Uptake Value as a Metabolic Predictor of Bone Marrow Response to Radiation: Impact on Acute and Late Hematological Toxicity in Cervical Cancer Patients Treated With Chemoradiation Therapy

Purpose: To quantify the relationship between bone marrow (BM) response to radiation and radiation dose by using {sup 18}F-labeled fluorodeoxyglucose positron emission tomography [{sup 18}F]FDG-PET standard uptake values (SUV) and to correlate these findings with hematological toxicity (HT) in cervical cancer (CC) patients treated with chemoradiation therapy (CRT). Methods and Materials: Seventeen women with a diagnosis of CC were treated with standard doses of CRT. All patients underwent pre- and post-therapy [{sup 18}F]FDG-PET/computed tomography (CT). Hemograms were obtained before and during treatment and 3 months after treatment and at last follow-up. Pelvic bone was autosegmented as total bone marrow (BM{sub TOT}). Active bone marrow (BM{sub ACT}) was contoured based on SUV greater than the mean SUV of BM{sub TOT}. The volumes (V) of each region receiving 10, 20, 30, and 40 Gy (V{sub 10}, V{sub 20}, V{sub 30}, and V{sub 40}, respectively) were calculated. Metabolic volume histograms and voxel SUV map response graphs were created. Relative changes in SUV before and after therapy were calculated by separating SUV voxels into radiation therapy dose ranges of 5 Gy. The relationships among SUV decrease, radiation dose, and HT were investigated using multiple regression models. Results: Mean relative pre-post-therapy SUV reductions in BM{sub TOT} and BM{sub ACT} were 27% and 38%, respectively. BM{sub ACT} volume was significantly reduced after treatment (from 651.5 to 231.6 cm{sup 3}, respectively; P<.0001). BM{sub ACT} V{sub 30} was significantly correlated with a reduction in BM{sub ACT} SUV (R{sup 2}, 0.14; P<.001). The reduction in BM{sub ACT} SUV significantly correlated with reduction in white blood cells (WBCs) at 3 months post-treatment (R{sup 2}, 0.27; P=.04) and at last follow-up (R{sup 2}, 0.25; P=.04). Different dosimetric parameters of BM{sub TOT} and BM{sub ACT} correlated with long-term hematological outcome. Conclusions: The volumes of BM{sub TOT} and BM{sub ACT} that are exposed to even relatively low doses of radiation are associated with a decrease in WBC counts following CRT. The loss in proliferative BM SUV uptake translates into low WBC nadirs after treatment. These results suggest the potential of intensity modulated radiation therapy to spare BM{sub TOT} to reduce long-term hematological toxicity.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2024

A generative artificial intelligence framework based on a molecular diffusion model for the design of metal-organic frameworks for carbon capture

Metal-organic frameworks (MOFs) exhibit great promise for CO 2 capture. However, finding the best performing materials poses computational and experimental grand challenges in view of the vast chemical space of potential building blocks. Here, we introduce GHP-MOFassemble, a generative artificial intelligence (AI), high performance framework for the rational and accelerated design of MOFs with high CO 2 adsorption capacity and synthesizable linkers. GHP-MOFassemble generates novel linkers, assembled with one of three pre-selected metal nodes (Cu paddlewheel, Zn paddlewheel, Zn tetramer) into MOFs in a primitive cubic topology. GHP-MOFassemble screens and validates AI-generated MOFs for uniqueness, synthesizability, structural validity, uses molecular dynamics simulations to study their stability and chemical consistency, and crystal graph neural networks and Grand Canonical Monte Carlo simulations to quantify their CO 2 adsorption capacities. We present the top six AI-generated MOFs with CO 2 capacities greater than 2m mol g -1 , i.e., higher than 96.9% of structures in the hypothetical MOF dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Morse-Smale Analysis of Ion Diffusion in Ab Initio Battery Materials Simulations

Ab initio molecular dynamics (AIMD) simulations are increasingly useful in modeling, optimizing and synthesizing materials in energy sciences. In solving Schrödinger’s equation, they generate the electronic structure of the simulated atoms as a scalar field. However, methods for analyzing these volume data are not yet common in molecular visualization. The Morse-Smale complex is a proven, versatile tool for topological analysis of scalar fields. In this paper, we apply the discrete Morse-Smale complex to analysis of first-principles battery materials simulations. We consider a carbon nanosphere structure used in battery materials research, and employ Morse-Smale decomposition to determine the possible lithium ion diffusion paths within that structure. Our approach is novel in that it uses the wavefunction itself as opposed distance fields, and that we analyze the 1-skeleton of the Morse-Smale complex to reconstruct our diffusion paths. Furthermore, it is the first application where specific motifs in the graph structure of the complete 1-skeleton define features, namely carbon rings with specific valence. We compare our analysis of DFT data with that of a distance field approximation, and discuss implications on larger classical molecular dynamics simulations.

25 ENERGY STORAGE↗

DOE OSTI2018

Red Emitting Monoazo Disperse Dyes with Phenyl(1H-benzoimidazol-5-yl) Methanone as Inbuilt Photostabilizing Unit: Synthesis, Spectroscopic, Dyeing and DFT Studies

Synthesis of three novel phenyl(1H-benzoimidazol-5-yl)methanone based fluorescent monoazo disperse dyes and their characterization by spectroscopic methods ({sup 1}H NMR, {sup 13}C NMR, IR and MS) are presented. Insertion of phenyl(1H-benzoimidazol-5-yl)methanone moiety bring about induced fluorescence properties and enhanced photostability as compared to the previously reported analogues (CI Solvent Yellow 14, 4-diethylamino-2-hydroxy-1-diazobenzene and 7-(diethylamino)-4-hydroxy-3-(phenyldiazenyl)-2H-chromen-2-one). Synthesized phenyl(1H-benzoimidazol-5-yl)methanone based dyes exhibited red-shifted absorption maxima (497–516 nm), high molar extinction coefficients and are emitting in the far-red region (565–627 nm). Moreover, naphthalene-comprising dyes showed negative solvatochromism while N,N-diethylamine comprising dyes showed positive solvatochromism and are in good agreement with solvent polarity graphs and the computed energy levels of highest occupied and lowest unoccupied molecular orbitals. Synthesised dyes have better photostability (light fastness) and sublimation fastness on dyed polyester and nylon compared to reported analogues. DFT calculated energies, electrophilicity index and Frontier Molecular Orbitals (FMO’s) enabled to evaluate the stabilities of azo and hydrazone forms of the dyes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Adaptive continuity-preserving simplification of street networks

Street network data is widely used to study human-based activities and urban structure. Often, these data are geared towards transportation applications, which require highly granular, directed graphs that capture the complex relationships of potential traffic patterns. While this level of network detail is critical for certain fine-grained mobility models, it represents a hindrance for studies concerned with the morphology of the street network. For the latter case, street network simplification — the process of converting a highly granular input network into its most simple morphological form — is a necessary, but highly tedious preprocessing step, especially when conducted manually. In this manuscript, we develop and present a novel adaptive algorithm for simplifying street networks that is both fully automated and able to mimic results obtained through a manual simplification routine. The algorithm — available in the neatnet Python package — outperforms current state-of-the-art procedures when comparing those methods to manually, human-simplified data, while preserving network continuity.

Python↗

DOE OSTI2020

Decentralized Schemes with Overlap for Solving Graph-Structured Optimization Problems

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it uses overlapping subdomains to promote and accelerate convergence. We show that the algorithm converges if the size of the overlap is sufficiently large and that the convergence rate improves exponentially with the size of the overlap. The proposed approach provides a bridge between fully decentralized and centralized architectures and is flexible in that it enables the implementation of asynchronous schemes, handling of constraints, and balancing of computing, communication, and data privacy needs. The proposed scheme is tested in an estimation problem for a 9241-node power network and we show that it outperforms the alternating direction method of multipliers.

asynchronous↗

DOE OSTI2024

Graph-learning approach to combine multiresolution seismic velocity models

SUMMARY The resolution of velocity models obtained by tomography varies due to multiple factors and variables, such as the inversion approach, ray coverage, data quality, etc. Combining velocity models with different resolutions can enable more accurate ground motion simulations. Toward this goal, we present a novel methodology to fuse multiresolution seismic velocity maps with probabilistic graphical models (PGMs). The PGMs provide segmentation results, corresponding to various velocity intervals, in seismic velocity models with different resolutions. Further, by considering physical information (such as ray path density), we introduce physics-informed probabilistic graphical models (PIPGMs). These models provide data-driven relations between subdomains with low (LR) and high (HR) resolutions. Transferring (segmented) distribution information from the HR regions enhances the details in the LR regions by solving a maximum likelihood problem with prior knowledge from HR models. When updating areas bordering HR and LR regions, a patch-scanning policy is adopted to consider local patterns and avoid sharp boundaries. To evaluate the efficacy of the proposed PGM fusion method, we tested the fusion approach on both a synthetic checkerboard model and a fault zone structure imaged from the 2019 Ridgecrest, CA, earthquake sequence. The Ridgecrest fault zone image consists of a shallow (top 1 km) high-resolution shear-wave velocity model obtained from ambient noise tomography, which is embedded into the coarser Statewide California Earthquake Center Community Velocity Model version S4.26-M01. The model efficacy is underscored by the deviation between observed and calculated traveltimes along the boundaries between HR and LR regions, 38 per cent less than obtained by conventional Gaussian interpolation. The proposed PGM fusion method can merge any gridded multiresolution velocity model, a valuable tool for computational seismology and ground motion estimation.

Geochemistry & Geophysics↗

DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Development of Ambient Mass Spectrometry Rapid Analysis Methods for Trace Inorganics

Ambient mass spectrometry is being investigated as a new method for rapidly characterizing trace inorganic species, including nuclear materials. SRNL is currently developing electrospray ionization (ESI) and paper spray ionization (PSI) methods for mass spectrometry for the detection of trace inorganic compounds JEOL AccuTOF™-DART ® LP 4G mass spectrometer. Sample analysis generates a complex three-dimensional data set with 10 2 -10 3 individual mass spectra spread temporally. To improve the quality and ease of data extraction from this amount of information, a simple data analysis pipeline written in R/R Studio has been improved and expanded upon. Specifically, the software now has header inputs to set base input/output filenames, isotopes of interest, and a list of concentrations analyzed on the instrument. Using list-based structures to enable batch processing of many concentrations at once, it then loads each file, extracts the relevant intensities for masses of interest from each spectrum, and iterates through each concentration to generate graphs of internal standard & analyte correlations, measured isotope ratios, and total ion chromatograms. It then filters the data to remove points at background levels or at the detector saturation limit. Using this filtered data, the pipeline re-creates the graphs to reveal high-quality information from a low-quality raw dataset. All graphs of the R software then output to PowerPoint format. Additionally, faster 3D visualization functionality was added to the pipeline for viewing the entire data file produced by the instrument as an intensity map. With these data analysis tools ready, samples of strontium nitrate/yttrium nitrate as an analyte/internal standard combination were measured on the AccuTOF. From the filtered data, calibration curves were prepared and limits of detection (LOD) of 1 ppb for ESI-MS and 20 ppb for PSI-MS were obtained. The quality available from the calibration curves and the low limits of detection demonstrate the value of the instrument/analysis pipeline system in characterizing trace inorganics.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Recombination smooths the time-signal disrupted by latency in within-host HIV phylogenies

Within-host HIV evolution involves several features that may disrupt standard phylogenetic reconstruction. One important feature is re-activation of latently integrated provirus, which has the potential to disrupt the temporal signal, leading to variation in the branch lengths and apparent evolutionary rates in a tree. Yet, real within-host HIV phylogenies tend to show clear, ladder-like trees structured by the time of sampling. Another important feature is recombination, which violates the fundamental assumption that evolutionary history can be represented by a single bifurcating tree. Thus, recombination complicates the within-host HIV dynamic by mixing genomes and creating evolutionary loop structures that cannot be represented in bifurcating trees. In this paper, we develop a coalescent-based simulator of within-host HIV evolution that includes latency, recombination, and effective population size dynamics that allows us to study the relationship between the true, complex genealogy of within-host HIV evolution, encoded as an Ancestral Recombination Graph (ARG), and the observed phylogenetic tree. To compare our ARG results to the familiar phylogeny format, we calculate the expected bifurcating tree after decomposing the ARG into all unique site trees, their combined distance matrix, and the overall corresponding bifurcating tree. While latency and recombination separately disrupt the phylogenetic signal, remarkably, we find that recombination recovers the temporal signal of within-host HIV evolution caused by latency by mixing fragments of old, latent genomes into the contemporary population. In effect, recombination averages over extant heterogeneity, whether it stems from mixed time-signals or population bottlenecks. Further, we establish that the signals of latency and recombination can be observed in phylogenetic trees despite being an incorrect representation of the true evolutionary history. Using an Approximate Bayesian Computation method, we develop a set of statistical probes to tune our simulation model to nine longitudinally-sampled within-host HIV phylogenies. Because ARGs are exceedingly difficult to infer from real HIV data, our simulation system allows investigating effects of latency, recombination, and population size bottlenecks by matching decomposed ARGs to real data as observed in standard phylogenies.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Optimal Control of a Degenerate PDE for Surface Shape

Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape in this paper. Specifically, we consider an objective (tracking) functional for surface shape with the prescribed mean curvature equation in graph form as a state constraint. The control variable is the prescribed curvature. We prove existence of an optimal control, and using improved regularity estimates, we show sufficient differentiability to make sense of the first order optimality conditions. This allows us to rigorously compute the gradient of the objective functional for both the continuous and discrete (finite element) formulations of the problem. Numerical results are shown to illustrate the minimizers and optimal controls on different domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗