Estimating Uncertainty of Neural Network Predictions for Inelastic Mechanical Deformation using Coupled FEM-NN Approach
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Context.Nuclear networks are widely used coupled with hydrodynamical simulations of explosive scenarios to account for the change of nuclear species and energy generation rate due to nuclear reactions. In this way, there is a feedback mechanism between the hydrodynamical state and the nuclear processes. Unfortunately, the timescale of nuclear reactions is orders of magnitude smaller than the dynamical timescale that drives hydrodynamical simulations. Therefore, these nuclear networks are usually very small, reduced in most cases to a dozen elements, especially when simulations are carried out in more than one dimension. Aims.We present here an extended nuclear network, with 90 species, designed for being coupled with hydrodynamic simulations, which includes neutrons, protons, electrons, positrons, and the corresponding neutrino and anti-neutrino emission. This network is also coupled with temperature, making it extremely robust and, together with its size, unique of its kind. The inclusion of electron captures on free protons makes the network very appropriate for multidimensional studies of Type Ia supernova explosions, especially when the exploding object is a massive white dwarf. Methods.We perform several tests that are relevant to simulate explosive scenarios, such as Type Ia supernovae and core-collapse supernovae. We compare the results of the 90 nuclei network with a standardα-chain network with 14 elements to evaluate the differences in the energy generation rate. We also evaluate the relevance of including the electrons in the network in terms of generated yields and how it affects the pressure of a degenerate fluid such as that of white dwarfs. The results obtained with the 90-nuclei network have been verified with a much larger 2000-nuclei network built from REACLIB (WinNet), in terms of nuclear energy generation rate, pressure, and produced yields. Results.The results obtained with the proposed medium-sized network compare fairly well, to a few percent, with those computed withWinNetin scenarios reproducing the gross physical conditions of current Type Ia supernova explosion models. In those cases where the carbon and oxygen fuel ignites at high density, the high-temperature plateau typical of the nuclear statistical equilibrium regime is well defined and stable, allowing large integration time steps. We show that the inclusion of electron captures on free protons substantially improves the estimation of the electron fraction of the mixture. Therefore, the pressure is better determined than in networks where electron captures are excluded, which will ultimately lead to more reliable hydrodynamic models. Explosive combustion of helium at low density, occurring near the surface layer of a white dwarf, is also better described with the proposed network, which gives nuclear energy generation rates much closer toWinNetthan typical reduced alpha networks. Conclusions.A nuclear network withN= 90 species, including electrons, aimed at multidimensional calculations of supernova explosions is described and verified. The proposed network is suitable for the study of Type Ia supernova explosions because it provides better values of pressure and electron abundance than other existing networks with smaller or even a similar size but without including electron capture processes.
Modern distribution systems energized by inverter-interfaced distributed generators (DGs) operate as coupled cyber-physical networks (C/P-networks), where the controllable components in the physical network (P-network) are coordinated through the cyber network (C-network). The concept of dynamic microgrids (MGs) operation has been adopted to enable distribution system autonomous operation with varying electric boundaries. To further enhance system operation resiliency and flexibility, dynamic MGs operation with reconfigurable C/P-networks is discussed in this work. An evaluation framework is proposed to assess the operational feasibility of distribution feeders with multiple inverter-based dynamic MGs and come out with possible restoration solutions in the context of cross-layer C/P-network reconfiguration. Furthermore, distributed controllers are developed for components with different operating characteristics to realize seamless system topology variations and provide coordinated secondary regulation in various operation modes. Furthermore, the proposed evaluation framework along with the developed distributed controller has been validated using a Hardware-in-the-Loop (HIL) real-time CPS testbed.
In this paper, different pore network models to simulate single-phase flow in porous media are built and their accuracy is evaluated. In addition to the conventional pore network model (CPNM) which consists of regular pore bodies and throat bonds, three improved pore network models (IPNMs) are developed allowing to better describing the real pore and throat geometry. The first improved pore network model (IPNM1) replaces the regular throat bond with a throat bond showing the real throat cross section. The second improvement (IPNM2) uses a series of sub-throat bonds with varying cross sections to better describe the real throat geometry, which is firstly proposed in this paper. The third model (IPNM3) extracts the real pore-throat-pore geometry without simplification. The conductance of fluid flow through these more realistic throat bonds is calculated by the lattice Boltzmann method (LBM). The accuracy and computational efficiency of the different pore network models are evaluated taking the LBM simulation over the whole porous medium as reference solution. The global permeability and detailed pressure distributions in the pores for the different pore network models are validated. The results show that the accuracy of the pore network model increases from CPNM to IPNM3, but at the expense of increasing computational cost. This study suggests that IPNM3 can replace a whole-domain LBM simulation with similar accuracy but much lower computational cost. As a first-order approximation the newly proposed IPNM2 is suggested as good compromise between accuracy and computational cost.
Hybrid magnonic systems have emerged as versatile modular components for quantum signal transduction and sensing applications owing to their capability of connecting distinct quantum platforms. To date, the majority of the magnonic systems have been explored in a local, near-field scheme, due to the close proximity required for realizing a strong coupling between magnons and other excitations. This constraint greatly limits the applicability of magnons in developing remotely coupled, distributed quantum network systems. On the contrary, opto-electronic architectures hosting self-sustained oscillations have been a unique platform for long-haul signal transmission and processing. Here, we integrated an opto-electronic oscillator with a magnonic oscillator consisting of a microwave waveguide and a Y 3 Fe 5 O 12 (YIG) sphere, and demonstrated strong and coherent coupling between YIG’s magnon modes and the opto-electronic oscillator’s characteristic photon modes—revealing the hallmark anti-crossing gap in the measured spectrum. In particular, the photon mode is produced on-demand via a nonlinear, parametric process as stipulated by an external seed pump. Both the internal cavity phase and the external pump phase can be precisely tuned to stabilize either degenerate or nondegenerate auto-oscillations. Our result lays out a new, hybrid platform for investigating the long-distance coupling and nonlinearity in coherent magnonic phenomena, which may be found useful in constructing the future “distributed hybrid magnonic systems.”
The Department of Defense (DoD) faces the substantial challenge of cost-effectively retrofitting one to two installations per month, each comprising approximately 1,000 buildings, to improve resilience, reduce energy consumption, and enhance energy supply security. Achieving these objectives requires optimal system selection and effective risk mitigation during system integration. To address this need, we introduce Platform-Based Design (PBD), a structured, hierarchical methodology adapted from other industrial sectors to the domain of energy system retrofits. We demonstrate the effectiveness of PBD through a techno-economic feasibility study comparing geothermal-coupled thermal energy networks (TENs) with conventional energy systems for heating, cooling, and powering 17 buildings at Joint Base Andrews (JBA) in Maryland. Our analysis illustrates that the PBD approach enables rigorous, data-driven, sequential decision making, resulting in a family of Pareto-optimal systems, among which the TEN emerged as the most promising solution. The selected TEN design integrates geothermal borefields, heat recovery heat pumps, photovoltaic (PV) arrays, and battery storage. Compared to the baseline system – gas heating combined with air-source chillers – the proposed TEN reduces annual imported energy by 74% and peak electricity demand by 45%, achieves a levelized cost of energy of $\$0.210$/kWh, and substantially enhances resilience. Life-cycle costs increase by approximately 6%, and initial investment costs are about 2.5 times higher than the baseline. However, if central plant infrastructure, district loops, and utility-scale PV and battery systems are privately funded and operated, the initial investment would fall below the baseline system cost. Critical to achieving these significant performance improvements were detailed nonlinear dynamic simulations coupling geothermal heat transfer, energy system operation, and realistic feedback control logic. These simulations identified essential design modifications and control strategy refinements that substantially reduced energy use, peak demand, and compressor shortcycling, thereby improving durability and reliability—issues that would have been significantly more expensive to resolve during operation. Additionally, the verification step highlighted sensitivities to key design parameters that could reduce initial investment by approximately $\$2$ million and reduce annual life-cycle costs more than $\$300,000$. We recommend adopting the PBD methodology for future feasibility studies and TEN pilot projects to gain valuable operational experience. Furthermore, we recommend that DoD invest in transferring and scaling the PBD methodology to other installations. This entails developing standardized computational frameworks and component libraries as well as training industry in conducting PBD. Such investments would enable rapid, robust, reliable, and cost-effective retrofits, supporting DoD’s ambitious energy system modernization goals.
The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. However, such a joint optimization is known as a challenging problem with complex network constraints and couplings of electric, hydraulic, and thermal models that are nonlinear and nonconvex. We formulate an optimal power-water-heat flow (OPWHF) problem and develop a computationally efficient heuristic to solve it. The proposed heuristic decomposes OPWHF into subproblems, which are iteratively solved via convex relaxation and convex-concave procedure. Simulation results validate that the proposed framework can improve operational flexibility and social welfare of the integrated system, wherein the water and heating networks respond as virtual energy storage to time-varying energy prices and solar photovoltaic generation. Moreover, we perform sensitivity analysis to compare two modes of heating network control: by flow rate and by temperature. Our results reveal that the latter is more effective for heating networks with a wider space of pipeline parameters.
We present a combined experimental and theoretical study of the mineral atacamite Cu 2 Cl(OH) 3 . Density-functional theory yields a Hamiltonian describing anisotropic sawtooth chains with weak 3D connections. Experimentally, we fully characterize the antiferromagnetically ordered state. Here, magnetic order shows a complex evolution with the magnetic field, while, starting at 31.5 T, we observe a plateaulike magnetization at about M sat /2. Based on complementary theoretical approaches, we show that the latter is unrelated to the known magnetization plateau of a sawtooth chain. Instead, we provide evidence that the magnetization process in atacamite is a field-driven canting of a 3D network of weakly coupled sawtooth chains that form giant moments.
A system and method includes an operational network that communicates with an external network by opening a first transmission protocol socket. A data diode coupled to the operational network and a gateway enables the one-way transfer of all information received from the external network and transmitted by the operational network to the gateway such that no information travels from the gateway to the operational network or the external network. The gateway opens a second transmission protocol socket by mapping a sequence number to an acknowledgement number and increasing that mapped acknowledgement number by a value of one. A transmitter then transmits the acknowledgment to a remote network or a gateway.
Virtual water flows are used to map the indirect water consumption connections implied by the supply chain of a city, region, or country. This information can be used to manage supply chains to achieve environmental policy objectives and mitigate environmental risks to critical supply chains. A limitation of prior work is that these flows are typically analyzed using monolayer networks, which ignores crucial intersectoral or interlayer couplings. Here, in this study, we use a multilayer network to account for such couplings when analyzing blue virtual water flows in the United States. Our multilayer network consists of 115 different regions (nodes), covering the entire conterminous United States; 41 coupled economic sectors (layers); and ∼2 × 10 7 possible links. To analyze the multilayer network, we focus on three fundamental network properties: topological connectivity, mesoscale structure, and node centrality. The network has a high connectivity, with each node being on average connected to roughly 2/3 of the network's nodes. Interlayer flows are a major driver of connectivity, representing ∼54% of all the network's connections. Five different groups of tightly connected nodes (communities) characterize the network. Each community represents a preferred spatial mode of long-range virtual water interaction within the United States. We find that large (populous) cities have a stronger influence than small ones on network functioning because they attract and recirculate more virtual water through their supply chains. Our results also highlight differences between the multilayer and monolayer virtual water network, which overall show that the former provides a more realistic representation of virtual water flows.
Abstract Liquid crystalline elastomers (LCEs) are stimuli‐responsive materials capable of undergoing large deformations. The thermomechanical response of LCEs is attributable to the coupling of polymer network properties and disruption of order between liquid crystalline mesogens. Complex deformations have been realized in LCEs by either programming the nematic director via surface‐enforced alignment or localized mechanical deformation in materials incorporating dynamic covalent chemistries. Here, the preparation of LCEs via thiol‐Michael addition reaction is reported that are amenable to surface‐enforced alignment. Afforded by the thiol‐Michael addition reaction, dynamic covalent bonds are uniquely incorporated in chemistries subject to surface‐enforce alignment. Accordingly, LCEs prepared with complex director profiles are able to be programmed and reprogrammed by (re)activating the dynamic covalent chemistry to realize distinctive shape transformations.
Here, this study investigates the contribution of fluid saturation variation to the time-lapse velocity response by performing fluid substitution modeling. The methodology is exemplified by the time-lapse seismic monitoring of carbon dioxide at Farnsworth field unit (FWU). In order to evaluate the fluid distribution in a matured oil reservoir, the Southwest Regional Partnership (SWP) acquired multiple vertical seismic profile (VSP) surveys at different times during the CO 2 –water alternatinggas (WAG) injection period. In this work, we present a thorough methodology for computing the elastic response of the saturated rock for different fluid saturations using a site-specific petro-elastic model (PEM). The output from the PEM was combined with results from a fluid compositional model to compute the seismic velocities at times corresponding to each VSP survey. To produce a calibrated simulated response, the measured time-lapse seismic velocities were integrated into the numerical simulation model. The mismatches between the predicted and measured time-lapse velocities were minimized through an iterative calibration process using a trained artificial neural network proxy (ANN) coupled with a particle swarm optimizer (PSO). Our study indicates that the hybrid optimization workflow can effectively perform the history matching. With an accurate prediction of the hydrodynamic properties, the migration of CO 2 within the subsurface was modeled by predicting the spatial velocity distribution for a radius of 305 m around the injection well. The technology demonstrated and the expertise gained from this study can guide similar CO 2 -WAG projects.
The interplay of nematicity and superconductivity has been observed in a wide variety of quantum materials. To explore this interplay, we consider a two-dimensional (2D) array of nematogens, local droplets with Z 3 nematicity, coupled to a network of Josephson junction wires. Using finite temperature classical Monte Carlo simulations, we elucidate the phase diagram of this model and show that the development of superconducting correlations and the directional delocalization of Cooper pairs can promote nematogen ordering, resulting in long-range nematic order. We obtain the transport properties of our model within an effective resistor network picture. We discuss these ideas in the context of the 2D electron gas at the (111) KTaO 3 interface and the doped topological insulators Nb x Bi 2 Se 3 and Cu x Bi 2 Se 3 . Overall, our work makes contact with Phil Anderson’s numerous contributions to broken symmetries driven by the saving of kinetic energy, including double exchange ferromagnetism and the interlayer tunneling theory of high Tc csuperconductivity.
Carbon dioxide-Enhanced Oil Recovery (CO 2 -EOR) is known as one of techniques for hydrocarbon production improvement as wells as an important candidate to reduce greenhouse gas emissions. Thus, an ideal development strategy for a CO 2 -EOR project would consider multiple objectives including to maximize oil recovery, CO 2 storage volume and project economic outcomes. This work proposes a robust computational framework that couples artificial neural network (ANN) and multi-objective optimizers to optimize the aforementioned objectives in CO 2 -EOR processes simultaneously. Expert ANN systems are trained and employed as surrogate models of the high-fidelity compositional simulator in the optimization workflow. The robustness of the development optimization protocol is confirmed via a synthetic injection-pattern-base case study. Afterward a field implementation to Morrow-B formation to optimize the tertiary recovery stage of the field development is discussed. This work compares the optimum solution found using an aggregate objective function and the solution repository (Pareto front) generated by the multi-objective optimization process. The comparison indicates the existence of potential multi-solutions satisfying certain criteria in a CO 2 -EOR project designing, which cannot be found using traditional weighted sum method. The optimization results provide significant insight into the decision-making process of CO 2 -EOR project when multiple objective functions are considered.
A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction rates and transition-state ensembles. Under the framework of transition path theory, Rotskoff et al. [Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, Proceedings of Machine Learning Research (PLMR, 2022), Vol. 145, pp. 757–780] proposes an algorithm where a feedback loop couples a neural network that models the committor function with importance sampling, mainly umbrella sampling, which collects data needed for adaptive training. Here, in this work, we show additional modifications are needed to improve the accuracy of the algorithm. The first modification adds elements of supervised learning, which allows the neural network to improve its prediction by fitting to sample-mean estimates of committor values obtained from short molecular dynamics trajectories. The second modification replaces the committor-based umbrella sampling with the finite-temperature string (FTS) method, which enables homogeneous sampling in regions where transition pathways are located. We test our modifications on low-dimensional systems with non-convex potential energy where reference solutions can be found via analytical or finite element methods, and show how combining supervised learning and the FTS method yields accurate computation of committor functions and reaction rates. We also provide an error analysis for algorithms that use the FTS method, using which reaction rates can be accurately estimated during training with a small number of samples. The methods are then applied to a molecular system in which no reference solution is known, where accurate computations of committor functions and reaction rates can still be obtained.
A recently developed technique of transmission-mode microwave impedance microscopy (T-MIM) has greatly extended the capabilities of standard reflection-mode MIM to novel applications, such as the in operando study of nanoscale electro-acoustic devices. As is common for new techniques, systematic design principles for boosting sensitivity and balancing bandwidth are lacking. Here, we show numerically and analytically that the T-MIM signal is proportional to the reflection-mode voltage enhancement factor η of the circuit, as long as the output impedance of the local voltage source is properly treated. We show that this proportionality holds in the currently achievable “weak sampling” regime and beyond, for which we demonstrate a realistic path with commercially available superconducting components and critically coupled impedance matching networks. Furthermore, we demonstrate that for these next-generation designs, the sensitivity is generally maximized at a slightly different frequency from the unloaded S 11 resonance, which can be explained by the maximum power transfer theorem.
In a controlled cyber-physical network, such as a power grid, any malicious data injection in the sensor measurements can lead to widespread impact due to the actions of the closed-loop controllers. While fast identification of the attack signatures is imperative for reliable operations, it is challenging to do so in a large dynamical network with tightly coupled nodes. A particularly challenging scenario arises when the cyberattacks are strategically launched during a grid stress condition, caused by non-malicious physical disturbances.