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At least 397 records · Page 22

Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions

Here, in this paper, we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two weak formulations. For the strong formulation, the solution is directly parameterized with a neural network and optimized by minimizing the PDE residual. It can be proved that the convergence of the optimization problem guarantees the convergence of the approximate solution in the $L^1$ sense. The weak formulations are derived following (Brenier in Examples of hidden convexity in nonlinear PDEs, 2020) which characterizes the very weak solutions of QPME. Specifically speaking, the solutions are represented with intermediate functions who are parameterized with neural networks and are trained to optimize the weak formulations. Extensive numerical tests are further carried out to investigate the pros and cons of each formulation in low and high dimensions. This is an initial exploration made along the line of solving high-dimensional nonlinear PDEs with neural network-based methods, which we hope can provide some useful experience for future investigations.

97 MATHEMATICS AND COMPUTING↗

Benchmark study of the DTU OWC chamber with both two-way and one-way absorption

This paper reports on a benchmark study based on small-scale (1:50) measurements of a single, oscillating water column chamber mounted sideways in a long flume. The geometry of the OWC chamber is extracted from a barge-like, attenuator-type floating concept “KNSwing” with 40 chambers targeted for deployment in the Danish part of the North Sea. In addition to traditional two-way energy extraction we also consider one-way energy extraction with passive venting and compare chamber response, pressures and total absorbed energy between the two methods. A blind study was established for the numerical modeling, with participants applying several implementations of weakly nonlinear potential flow theory and commercial Navier–Stokes solvers (CFD). Both compressible and incompressible models were used for the air phase. Potential flow calculations predict more energy absorption near the chamber resonance for one-way absorption than for two-way absorption, but the opposite is found from the experimental measurements. This outcome is mainly attributed to energy losses in the experimental passive valve system, but this conclusion must be confirmed by better experimental measurements. Modeling the one-way valve in CFD proved to be very challenging and only one team was able to provide results which were generally closer to the experiments. The study illustrates the challenges associated with both numerical and experimental analysis of OWC chambers. Air compressibility effects were not found to be important at this scale, even with the large volume of additional air used for the one-way case.

16 TIDAL AND WAVE POWER↗

Applying Improved Optical Recognition with Machine Learning on Sorting Cu Impurities in Steel Scrap

Annually, 20–55 million tons of electronic waste (e-waste) is produced worldwide (5% of all municipal solid waste). Although e-waste embodies only 2% of America’s municipal waste, it accounts for a significantly larger proportion of the heavy metals and flame retardants present in the waste stream. Currently, less than 20% of all e-waste is recycled in the United States because the heterogeneity of the feedstock limits the opportunity for reuse in high value products and processing of the waste itself is often too costly to justify handling. To address this concern, the aims of this study are: 1) to identify the major plastic and metal compositions within electronic shredder residue (ESR), 2) to formulate solvents and processing conditions to separate 90% of the plastics targeted from consumer shred ESR, and 3) to develop a process design model to estimate the cost and energy efficiency of the proposed solvent-based processing. In this study, a pre-sorted heterogeneous ESR feedstock (one where aluminum, magnetic components, and hazardous battery materials removed by an e-waste recycling facility) was used, with the major compositions of the ESR characterized. It was found that 25 wt.% of the feedstock was composed of plastics, 6 wt.% rubber, 27 wt.% printed circuit boards, 23% wire, and the remainder metals and capacitors. Within the plastic portion, polystyrene (PS, 40 wt.%), acrylonitrile butadiene styrene (ABS, 25 wt.%), and styrene-acrylonitrile (SAN, 9wt.%) were identified to compose the majority of the screened plastics using Fourier transform infrared spectroscopy (FTIR). Next, selective solvents were screened using Hansen Solubility Parameter Theory (HSP) for dissolving PS and ABS. The pre-screening results show that methylene chloride (dichloromethane, DCM) and tetrahydrofuran (THF) are capable of dissolving the most PS and ABS, while methanol (MeOH) and ethylene glycol (EG) are capable of precipitating the most PS and ABS. These solvents were subsequently used to recover polymers and remove. flame retardants within the ESR feedstock. By optimizing the dissolution time and the solvents used, the highest polymer dissolution yield (99 wt.%%) was achieved using DCM for 48 hr. Both pre-screened anti-solvents (MeOH and EG) showed the highest polymer precipitation yield (71 wt.%). In terms of flame retardant removal rate, EG was found to have a high phosphorus-containing flame retardant removal rate (up to 98%). Characterization shows that the proposed solvent-based processing can preserve a high molecular weight fraction of the polymers and effectively remove flame retardants. Cost analysis indicates that the amount of the solvent/anti-solvent recovered after the reaction would play a critical role in reducing the operating costs. The energy analysis shows that the proposed solvent-based processes can save up to 60% of the embodied energy used to manufacture plastics used in electronics (PS and ABS were used for calculations). The results from this project prove the potential of solvent-based processing to produce secondary materials (plastics and metals) from e-waste for cross-industry reuse.

36 MATERIALS SCIENCE↗

Optimizing High-Throughput Inference on Graph Neural Networks at Shared Computing Facilities with the NVIDIA Triton Inference Server

Abstract With machine learning applications now spanning a variety of computational tasks, multi-user shared computing facilities are devoting a rapidly increasing proportion of their resources to such algorithms. Graph neural networks (GNNs), for example, have provided astounding improvements in extracting complex signatures from data and are now widely used in a variety of applications, such as particle jet classification in high energy physics (HEP). However, GNNs also come with an enormous computational penalty that requires the use of GPUs to maintain reasonable throughput. At shared computing facilities, such as those used by physicists at Fermi National Accelerator Laboratory (Fermilab), methodical resource allocation and high throughput at the many-user scale are key to ensuring that resources are being used as efficiently as possible. These facilities, however, primarily provide CPU-only nodes, which proves detrimental to time-to-insight and computational throughput for workflows that include machine learning inference. In this work, we describe how a shared computing facility can use the NVIDIA Triton Inference Server to optimize its resource allocation and computing structure, recovering high throughput while scaling out to multiple users by massively parallelizing their machine learning inference. To demonstrate the effectiveness of this system in a realistic multi-user environment, we use the Fermilab Elastic Analysis Facility augmented with the Triton Inference Server to provide scalable and high-throughput access to a HEP-specific GNN and report on the outcome.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Review on Low-Temperature Electrolytes for Lithium-Ion and Lithium Metal Batteries

Abstract Among various rechargeable batteries, the lithium-ion battery (LIB) stands out due to its high energy density, long cycling life, in addition to other outstanding properties. However, the capacity of LIB drops dramatically at low temperatures (LTs) below 0 °C, thus restricting its applications as a reliable power source for electric vehicles in cold climates and equipment used in the aerospace. The electrolyte engineering has proved to be one of the most effective approaches to mitigate LIB performance degradation at LTs. In this review, we summarize the important factors contributing to the deterioration in Li + transport and capacity utilization at LTs while systematically categorize the solvents, salts and additives reported in the literature. Strategies to improve the Li + transport kinetics, in the bulk electrolyte and across the interphases, are discussed. In particular, the formation mechanism of solid electrolyte interphase and its functionality for LT electrolytes are analyzed. Perspectives on the future evolution of this area are also provided. Graphical abstract

25 ENERGY STORAGE↗

Non-linear Wire Rope Isolator Model to Enhance Transportation Simulation of Fragile Equipment

Abstract Introduction Wire rope isolators are often used as means of vibration isolation for the transportation of fragile machine equipment. When deployed as suspension systems in a transportation scenario, a simple spring–damper model is often used to predict the dynamic loads that act on the structure being transported. However, this simple model has proved to be too simplistic to be used in the development of an accurate numerical model that can predict the vibration levels experienced by the inner components of fragile equipment during its transportation. This paper describes the experimental tests conducted on a wire rope isolator used for the transportation of the prototype SSR1 cryomodule. Materials and methods A hysteretic Bouc–Wen model has been used to analytically describe the force–deformation relationship of the wire rope isolators. The developed model of the isolator has been implemented in a larger model to simulate the actual transportation of the prototype SSR1 cryomodule, a section of the new PIP-II linear accelerator under construction at Fermilab. A series of multibody dynamic simulations with rigid and flexible components was used to numerically determine the acceleration of some critical components. Results and conclusions An actual experimental transportation was simulated using two numerical models: the developed Bouc–Wen model and a conventional spring–damper model. It is shown how the Bouc–Wen formulation of the isolator characteristics drastically improves the correspondence between experimental and simulated results if compared to a spring–damper model, especially in the range of 0–30 Hz which is the most critical for transportation problems.

42 ENGINEERING↗

Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

Abstract We prove, under mild conditions, the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model, both in batch gradient descent and stochastic gradient descent. We also discuss a Riemannian version of the Adam algorithm. We show numerical simulations of these algorithms on various benchmarks.

Whiting, Wes (ORCID:0000000247505060)↗

Scheduling and Performance of Asynchronous Tasks in Fortran 2018 with FEATS

Most parallel scientific programs contain compiler directives (pragmas) such as those from OpenMP (Hermanns in Parallel programming in Fortran 95 using openMP, 2002. School of Aeronautical Engineering, Universidad Politécnica de Madrid, España, 2011), explicit calls to runtime library procedures such as those implementing the Message Passing Interface (MPI) (in A message-passing interface standard version 4.0, 2021. https://www.mpi-forum.org/docs/mpi-4.0/mpi40-report.pdf), or compiler-specific language extensions such as those provided by CUDA (Ruetsch and Fatica in CUDA Fortran for scientists and engineers: best practices for efficient CUDA Fortran programming, Elsevier, 2013). By contrast, the recent Fortran standards empower developers to express parallel algorithms without directly referencing lower-level parallel programming models (Numrich in Parallel programming with co-arrays, CRC Press, 2018, and Curcic in Modern Fortran: building efficient parallel applications, Manning Publications, 2020). Fortran’s parallel features place the language within the Partitioned Global Address Space (PGAS) class of programming models. When writing programs that exploit data parallelism, application developers often find it straightforward to develop custom parallel algorithms. Problems involving complex, heterogeneous, staged calculations, however, pose much greater challenges. Such applications require careful coordination of tasks in a manner that respects dependencies prescribed by a directed acyclic graph. When rolling one’s own solution proves difficult, extending a customizable framework becomes attractive. Further, the paper presents the design, implementation, and use of the Framework for Extensible Asynchronous Task Scheduling (FEATS), which we believe to be the first task scheduling tool written in modern Fortran. We describe the benefits and compromises associated with choosing Fortran as the implementation language, and we propose ways in which future Fortran standards can best support the use case in this paper.

97 MATHEMATICS AND COMPUTING↗

High dimensional binary classification under label shift: phase transition and regularization

Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. Here, to bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that there exists a phase transition phenomenon: Under certain overparametrized regime, the classifier trained using imbalanced data outperforms the counterpart with reduced balanced data. Moreover, we investigate the impact of regularization to the label shift: The aforementioned phase transition vanishes as the regularization becomes strong.

binary classification↗

An iterative dynamic chemical stiffness removal method for reacting flow simulations

Abstract An iterative dynamic chemical stiffness removal method (IDCSR) based on quasi-steady-state approximation (QSSA) is proposed. The IDCSR method is built on a previously developed non-iterative method which has proved to work well for small timestep sizes. A novel iterative procedure is designed in IDCSR to enable explicit time integration of stiff chemistry at relatively large timestep sizes relevant to practical reacting flow simulations. The effectiveness of the iterative procedure is first demonstrated with a toy problem and homogeneous auto-ignition with fixed integration step sizes, showing that larger timestep sizes can be allowed for explicit time integration using IDCSR compared with the previous non-iterative method. IDCSR is then compared with existing explicit chemistry solvers for simulations of homogeneous auto-ignition and shows similar or lower computational cost but significantly higher accuracy across a wide range of timestep sizes. IDCSR is further combined with an automatic adaptive time-stepping scheme for simulations of 0-D homogeneous auto-ignition and a 2-D laminar lifted n -dodecane jet flame. For the 0-D auto-ignition simulations, IDCSR is shown to reduce both the error (by 43%–90%) and computational cost (by 6–15 times) compared with existing explicit solvers, while achieving speed-up factors of up to 400 compared with VODE for a wide range of timestep sizes and reaction mechanisms. For the 2-D jet flame simulations, speed-up factors of 15 and 31 for chemistry integration, and 5 and 9 for overall simulation, are achieved by IDCSR compared with CVODE with and without analytic Jacobian, respectively.

Xu, Chao (ORCID:0000000153074159)↗

Seismic signal augmentation to improve generalization of deep neural networks

Deep learning has emerged as an effective approach for seismic data processing in general, and for earthquake monitoring in particular. The ability of deep learning models to generalize beyond the training and validation data is important for comprehensive earthquake monitoring; this ability furthermore depends on the availability of a sufficiently large and complete training dataset. However, this requirement can prove challenging to meet due to significant effort and time for data collection and labeling. Data augmentation provides an efficient and effective approach for increasing the dimension of training samples and improving generalization to unseen samples. In this paper, we present augmentation methods appropriate for seismic waveforms and demonstrate their ability to reduce bias and increase performance. Furthermore, these augmentation methods can be applied to a wide range of deep learning applications designed for seismic data.

58 GEOSCIENCES↗

Nonconvex regularization for sparse neural networks

Convex ℓ 1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in this paper, a nonconvex regularization method is investigated in the context of shallow ReLU networks: We prove that in contrast to the convex approach, any resulting (locally optimal) network is finite even in the presence of infinite data (i.e., if the data distribution is known and the limiting case of infinite samples is considered). Moreover, here we show that approximation guarantees and existing bounds on the network size for finite data are maintained.

97 MATHEMATICS AND COMPUTING↗

Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness

Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which encode data into low-dimensional latent features on a collection of charts, preserving the topology and geometry of the data manifold. Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering n noisy training samples, along with their noise-free counterparts, on a d-dimensional manifold. By training autoencoders, we show that chart autoencoders can effectively denoise the input data with normal noise. We prove that, under proper network architectures, chart autoencoders achieve a squared generalization error in the order of n–$\frac{2}{d+2}$log 4 n, which depends on the intrinsic dimension of the manifold and only weakly depends on the ambient dimension and noise level. We further extend our theory on data with noise containing both normal and tangential components, where chart autoencoders still exhibit a denoising effect for the normal component. As a special case, our theory also applies to classical autoencoders, as long as the data manifold has a global parametrization. Furthermore, our results provide a solid theoretical foundation for the effectiveness of autoencoders, which is further validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗

Tool-workpiece stick-slip conditions and their effects on torque and heat generation rate in the friction stir welding

Friction stir welding (FSW) has found increased applications in automotive and aerospace industries due to its advantages of solid-state bonding, no fusion and melting, and versatility in various working conditions and material combinations. However, the relationship among processing parameters, material properties, and bonding extent and fidelity remains largely empirical, primarily because of the lack of the mechanistic understanding of the tool-workpiece frictional behavior that affects our subsequent understanding of microstructural evolution and interface bonding formation. While the tool-workpiece stick-slip condition is believed to dictate the resulting torque and heat generation rate during the welding process, it remains rare and elusive to conduct a quantitative experimental measurement of such interfacial field. On the other hand, numerical simulations based on Computational Fluid Dynamics (CFD) rely on ad hoc assumptions of interfacial pressure and shear-stress conditions, but predictions can only be validated via the medium- and far-range temperature field which is known to be insensitive to the interfacial frictional behavior. This work first presents a comparison among two CFD-based simulation methodologies and the Coupled Eulerian Lagrangian (CEL) model in finite element method, the last of which uses the Coulomb friction so that the stick-slip is naturally developed. Based on the Hill-Bower similarity relationship in the contact analysis, an analytical model is developed here to prove why a constant stick-slip fraction will be developed in the steady state, to correlate the stick-slip fraction to processing parameters such as the tool spin rate, and further to derive dimensionless functions for torque and heat-generation-rate predictions. Pros and cons of various numerical approaches in predicting stick-slip are discussed, and our analytical model has been found to agree well with our numerical simulation and literature experimental results. These analyses provide the critical strain-rate and temperature fields that are needed for the bonding analysis in our future work.

36 MATERIALS SCIENCE↗

Toward efficient elastocaloric systems: Predicting material thermal properties with high fidelity

A critical need to accurately model thermal behaviors of materials that exhibit strong elastocaloric effects, including predicting the effects themselves at varying stresses and temperatures, has been addressed using a simple and versatile physics-based approach. The key factor leading to the high precision is approximating the underlying elastic phase transition as a smooth modification of lattice entropy between coexisting phases. Once the phase transformation entropy is modeled to match experimentally measured strain as a function of temperature and applied stress, estimating the heat capacity, entropy, and isothermal entropy and adiabatic temperature changes in temperature-stress coordinates becomes straightforward. This approach provides insight into how thermal properties of elastocaloric materials vary through the transition based on strain measurements that are simple to perform and interpret. In addition to aiding in the rapid evaluation of new and existing elastocaloric materials, this advance is expected to prove invaluable for accurate heat transfer modeling aimed at designing efficient regenerative elastocaloric cooling devices.

36 MATERIALS SCIENCE↗

Response of 11 B enriched ZrB 2 ultra-high temperature ceramic to neutron irradiation at elevated temperatures

ZrB 2 , an ultra-high temperature ceramic (UHTC) is being considered for use in fusion reactor first-wall structures, yet its response to irradiation remains poorly understood. This study employed scanning/transmission electron microscopy (S/TEM), synchrotron X-ray diffraction (XRD), finite element calculations, and thermal property measurements to thoroughly investigate the neutron-irradiation effects on 11 B-enriched ZrB 2 . Neutron irradiations were conducted at 220 °C and 620 °C, with a neutron fluence of 2.2 × 10 25 neutron/m 2 (energy > 0.1 MeV), resulting in 3.9 dpa and 4200 appm He. The study revealed the unusual prevalence of prism loops and a > c anisotropic lattice swelling, likely linked to the low c/a ratio of ZrB 2 , leading to grain boundary microcracking. Reducing the grain sizes was effective in reducing intergranular cracking and macroscopic swelling. The observation of cavities in ZrB 2 irradiated at 620 °C, as opposed to 220 °C, prompts questions about the temperature at which vacancies in ZrB 2 become mobile, and the role of neutron absorption by 10 B in elevating irradiation temperatures. Isotopic enrichment in 11 B proves to be a viable strategy for mitigating helium production in transition-metal diborides, which is a critical consideration for nuclear applications. Irradiation-induced defects reduce the thermal diffusivity and conductivity of ZrB 2 by a factor of 4–9, which has important implications for its role as a plasma-facing material in fusion reactors that drive high heat fluxes through first-wall materials. Here, this comprehensive study lays the foundation for understanding ZrB 2 behavior under neutron irradiation and highlights important phenomena to consider for various material applications.

36 MATERIALS SCIENCE↗

Controlling substrate temperature with infrared heating to improve mechanical properties of large-scale printed parts

Additively manufactured parts made with polymer extrusion techniques can be 50-75% weaker in the z-direction (across layers) than in the x- and y-directions. This has been attributed to poor mobility of polymer chains and a low degree of entanglement across a cold deposition interface. This is particularly a challenge when printing large-scale parts, such as with the Big Area Additive Manufacturing (BAAM) system, because layer times can exceed several minutes. The current work presents a method for controlling the temperature of the substrate material on the BAAM just prior to deposition using infrared heating lamps. Additionally, long layer times were simulated by actively cooling the material following deposition of each layer. The effect of substrate temperature on the z-direction mechanical properties of 20% carbon fiber reinforced acrylonitrile butadiene styrene (ABS) was measured for an initial temperature ranging from 50 °C to 150 °C and a preheated temperature ranging from 150 °C to 220 °C. Infrared preheating proved to be very effective when applied to substrates that had cooled considerably, almost doubling the tensile strength and increasing the fracture toughness by a factor of 7x.

36 MATERIALS SCIENCE↗

Large-scale additive manufacturing of self-heating molds

Large-scale material extrusion additive manufacturing technology is becoming the new mainstream technology for scaled-up composite mold and die applications. This paradigm shift in composite processing technology is primarily driven by out-of-autoclave tooling applications, in which fiber reinforced composite molds with scaled-up sizes and embedded heating elements are attractive. The present research describes the design, manufacturing, and testing of self-heating composite molds fabricated via a large-scale pellet extrusion 3D printing machine with an integrated wire co-extrusion tool. Polycarbonate (PC) composites reinforced with carbon fiber (PC/CF; 20 wt.%) and glass fiber (PC/GF; 20 wt.%) were used to fabricate mold parts. Joule heating thermal test results showed that uniform temperatures (~100 °C) were achieved for both PC/CF and PC/GF mold surfaces, using a custom-made feedback control power supply and infrared thermography. Mechanical characterizations, including tensile and flexural testing were performed on the wire-embedded and un-wired PC/CF and PC/GF base specimens to investigate the impact of the fiber reinforcement as well as the embedded wires. In the direction of extrusion, the ultimate tensile stress of PC/CF was 105 MPa, and that of PC/GF was 73 MPa, while the neat PC value was 64 MPa. Inner-bead voids and interfacial gaps were observed and characterized via optical and scanning electron microscopy. The embedded wires and inner bead impacted the mechanical properties of the composites. Furthermore, the stiffness of the wire-embedded mold was still satisfactory, proving that the technology can be used to fabricate additively manufactured out-of-oven/autoclave molds.

36 MATERIALS SCIENCE↗