Conditional Sampling with Monotone GANs: From Generative Models to Likelihood-Free Inference
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Mathematics↗
SEARCH · Engineering Papers
Results for “monotonicity”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Integrated computational materials engineering with monotonic Gaussian process.
Abstract not provided.
Tran, Anh↗
A chemical kinetics theory for interpreting the non-monotonic temperature dependence of enzymatic reactions
Abstract. One notable observation of enzymatic chemical reactions is that, for a given abundance of enzymes and substrates, temperature increases cause reaction rates to first increase consistent with the Arrhenius relationship, then plateau, and finally fall off quickly to zero at high temperatures. While many mathematical functions have been used to describe this pattern, we here propose a chemical kinetics theory which successfully replicates this observation and provides insights into the processes responsible for these dynamics. The chemical kinetics theory combines the law of mass action, von Smoluchowski's diffusion-limited chemical reaction theory, and Eyring's transition state theory. This new theory reveals that the thermally reversible enzyme denaturation ensured by the ceaseless thermal motion of molecules and ions in an enzyme solution explains the plateau and subsequent decrease in chemical reaction rates with increasing temperature. The temperature-dependent affinity parameter (K) that relates enzymes and substrates through their binding also affects the shape of the emergent temperature response. We demonstrate that with an increase in substrate availability, K shifts the optimal temperature, where reaction rates plateau, towards higher values. Further, we show that the chemical kinetics theory accurately represents 12 sets of published enzyme assay data and includes the popular mechanistic model by Ratkowsky et al. (2005) as a special case. Given its good performance and solid theoretical underpinning, we believe this new theory will facilitate the construction of more mechanistic-based environmental biogeochemical models.
Tang, Jinyun↗
Implicit Graph Neural Networks: A Monotone Operator Viewpoint
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Baker, Justin↗
c -functions in higher-derivative flows across dimensions
In the context of gravitational theories describing renormalization group flows across dimensions via AdS/CFT, we study the role of higher-derivative corrections to Einstein gravity. We use the Null Energy Condition to derive monotonicity properties of candidate holographic central charges formed by combinations of metric functions. We also implement an entropic approach to the characterization of the four-derivative flows using the Jacobson-Myers functional and demonstrate, under reasonable conditions, monotonicity of certain terms in the entanglement entropy via the appropriate generalization of the Ryu-Takayanagi prescription. In particular, we show that any flow from a higher dimensional theory to a holographic CFT 2 satisfies a type of monotonicity. We also uncover direct relations between NEC-motivated and entropic central charges.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Explicit entropic proofs of irreversibility theorems for holographic RG flows
We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In particular, we consider flows within the same dimension and holographically reprove the c-, F -, and a-theorems in dimensions two, three, and four. We focus on the family of maximally spherical entangling surfaces, define a quasi-constant of motion corresponding to the breaking of conformal invariance, and use a properly defined distance between minimal surfaces to construct a holographic c-function that is monotonic along the flow. We then apply our method to the case of flows across dimensions: there, we reprove the monotonicity of flows from AdS D+1 to AdS 3 and prove the novel case of flows from AdS 5 to AdS 4 .
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Input specific neural networks
Neural networks have emerged as powerful tools for mapping between inputs and outputs. However, their black-box nature limits the ability to encode or impose specific structural relationships between inputs and outputs. Many scientific and engineering problems, such as constitutive modeling in solid mechanics, require networks that can enforce convexity, monotonicity, or other structural constraints to ensure physical consistency. Here, we introduce the Input Specific Neural Network (ISNN), a new architecture that enables multiple, distinct constraints to be imposed on different input subsets for scalar-valued outputs. This framework unifies convex, monotone–convex, monotone, and arbitrary mappings within a single network for the first time. Two ISNN architectures with analytical first- and second-order derivatives are developed. We demonstrate the performance on synthetic toy problems, inverse problems in isotropic hyperelasticity, and finite element simulations. ISNNs achieve improved extrapolation behavior, require fewer invariant inputs than standard input convex networks for polyconvex potentials, and enable significant computational savings via manual differentiation. We also show how ISNNs can be used to learn structural relationships between inputs and outputs via a binary gating mechanism. Particularly, ISNNs are employed to model a homogenized anisotropic free energy potential in a decoupled multiscale setting. The network learns whether or not the potential should be modeled as polyconvex and retains only the relevant layers while using the minimum number of inputs. ISNNs provide a flexible foundation for embedding structural priors into neural networks, enhancing both interpretability and stability. They are broadly applicable across computational mechanics and other scientific domains requiring constrained functional relationships.
Jadoon, Asghar A. [Univ. of Texas, Austin, TX (Uni↗
Stockmayer fluid simulations for viscosity and glass transition temperature of ionic liquids
We develop a Stockmayer fluid model for molecular dynamics simulations of ionic liquids that captures molecular polarization, ionic conductivity, viscosity, and glass transition temperature, using ethylammonium nitrate (EAN) as an example. The ions in EAN are treated as spheres interacting via the Lennard-Jones potential with an embedded point charge and a permanent dipole moment. We show that our simulation results for EAN are consistent with experimental data and then explore the effects of the molecular parameters on the viscosity of ionic liquids. Our results indicate that viscosity monotonically increases with ionic charge and dipole moment but non-monotonically changes with ionic diameter (or molar volume). This non-monotonic trend arises from the competition among the electrostatic interactions, molecular packing, and size asymmetry between the cation and anion. In conclusion, our model also shows that long-lived ion pairs result in higher viscosities.
Coarse-grained simulations↗
Can the angular scale of cosmic homogeneity be used as a cosmological test?
Abstract In standard cosmology, the cosmic homogeneity scale is the transition scale above which the patterns arising from non-uniformities – such as groups and clusters of galaxies, voids, and filaments – become indistinguishable from a random distribution of sources. Recently, different groups have investigated the feasibility of using such a scale as a cosmological test and arrived at different conclusions. In this paper, we complement and extend these studies by exploring the evolution of the spatial ( $$R_{\textrm{H}}$$ R H ) and angular ( $$\theta _{\textrm{H}}$$ θ H ) homogeneity scales with redshift, assuming a spatially flat, $$\varLambda $$ Λ -Cold Dark Matter universe and linear cosmological perturbation theory. We confirm previous results concerning the non-monotonicity of $$R_{\textrm{H}}$$ R H with the matter density parameter $$\varOmega _{\textrm{m0}}$$ Ω m0 but also show that it exhibits a monotonical behavior with the Hubble constant $$H_{0}$$ H 0 within a large redshift interval. More importantly, we find that, for $$z \gtrsim 0.6$$ z ≳ 0.6 , $$\theta _{\textrm{H}}$$ θ H presents a monotonical behavior with $$\varOmega _{\textrm{m0}}$$ Ω m0 , as well as for $$H_0$$ H 0 the entire redshift interval analyzed. We find also that the angular homogeneity scale is sensitive to $$H_{0}$$ H 0 , especially at higher redshifts. Using the currently available $$\theta _{\textrm{H}}$$ θ H measurements, we illustrate the constraints on the $$\varOmega _{\textrm{m0}}$$ Ω m0 – $$H_{0}$$ H 0 plane through a MCMC analysis and show the feasibility of using the angular homogeneity scale as a new, model-independent way to constrain cosmological parameters.
Physics↗
Foam Fracturing Study for Stimulation Development of Enhanced Geothermal Systems
This is a final technical report for the project: Foam Fracturing Study for Stimulation Development of Enhanced Geothermal Systems (EGS). The goal is to demonstrate the feasibility of foam fracturing in EGS applications. The project, led by Oak Ridge National Laboratory (ORNL), was conducted in collaboration with Temple University. The report describes the research activities with Task 1 at ORNL: foam fracturing testing system development and experimental study on foam fracturing, and Task 2 at Temple University: foam testing and foam characterization. Main findings are: 1. A foam fracturing test system has been developed at ORNL, which can be used to perform foam fracturing under pressure up to 6,000 psi. The system monitors foam density during fracturing online and is capable of testing materials in both monotonic and cyclic (up to 50 Hz) injections. 2. Foam fracturing tests were carried out on Charcoal black granite specimens with a blind borehole to the middle length. Two diameters of blind borehole were tested; G2 series: 9.53 mm and G3 series: 4.76 mm. N2-in-water foam was used with AOS as a surfactant. 3. There was a hole-size effect on fracture initiation pressure. The effect is smaller in the case of foam, which was influenced by the high penetrability of gas in foam. Breakdown pressure showed a behavior just as that of fracture pressure; namely an increased value for small hole samples, while the effect in water fracture was more impressive than in foam fracture. 4. Water mass was reduced in foam fracturing within similar range of breakdown pressures. In G2 series, it was decreased from 10.44 g for water fracturing to 5.17 g, representing more than 50% water reduction. Therefore, there is the potential to reduce water use in EGS stimulation through foam fracturing. 5. Use of cyclic injection has the potential to reduce the breakdown pressure and seismicity in EGS application. Experiments using 4-s cycle period found that specimens can be fractured with a low number of cycles. The fatigue pressure was approximately 64 - 77% of monotonic breakdown pressure for water fracturing and 58 - 94% of the breakdown pressure for foam fracturing. 6. A foam stability testing system has been developed that can test foam at 220 Deg C to 2,000 psi. Tested components of candidate foams included two gases: N2 and CO2; 4 surfactants: AOS, SDS, NP-40 and CTAC; 5 stabilizing agents: guar, bentonite clay, borate salt, silica NPs, and GO. 7. N2 and AOS provided the most stable performance over the tested ranges. Furthermore, the AOS foam with stabilizing agents of guar and borate salt (crosslinker) offered the highest half-life of 20 minutes at 200 Deg C and 1,000 psi. 8. Arrhenius equation and modified power law have been demonstrated to fit well the half-time vs. temperature and pressure data, respectively. These relations can be useful to provide the suggestion for future foam stability study. This submission contains the supporting data developed during the project: 1) A final technical report 2) Granite fracturing data in monotonic and cyclic injections with water and N2 foam Foam performance data in various temperatures and pressures, including half-time, is submitted separately.
15 GEOTHERMAL ENERGY↗
Foam Fracturing Study for Stimulation Development of Enhanced Geothermal Systems
The large thermal gradients and high subsurface temperatures of the western region of the U.S. hold great potential for the implementation of enhanced geothermal systems (EGS). The development of these potential EGS resources requires stimulation of the reservoir to enhance permeability and it has been widely reported that a substantial amount of water will be required should conventional hydraulic stimulation be used. This presents a huge challenge and a high risk to the geothermal development because the water stress1 in these areas is already high or extremely high. The use of foam, a gas/liquid mixture predominantly composed of gas, in fracturing is considered and explored in this project as a potential approach to address water concerns with hydraulic stimulation in the development of EGS. This project, led by Oak Ridge National Laboratory (ORNL) in collaboration with Temple University, was awarded in an open lab call in 2018, and was part of the DOE GTO waterless stimulation initiative. The goal of the project was to demonstrate the feasibility of foam fracturing for EGS development through two primary tasks: Task 1: Laboratory study of the effectiveness of foam fracturing for representative geological materials, including cyclic pressurization using foam (led by ORNL) and Task 2: High temperature foam material selection and characterization (led by Temple University). In FY19, ORNL finished the critical review on serval issues associated with foam fracturing and the implementation of the proposed tasks in a lab study (Wang, et al., 2019), and completed the foam fracturing testing using cement as a model material (Wang, et al, 2020a). The work at ORNL was geared up to develop a brand-new foam testing system in FY20. The purchase of main components for the new system was finished in the first half of the FY20. The assembly of the foam testing system and foam fracturing testing were completed in the second half of the FY20 (Wang, et al., 2021a). Task 1 required the development of a test system which can be used to perform hydraulic fracturing of geological specimens with both water and foamed liquids at pressure up to 6,000 psi (41.4 MPa). The system possesses several capabilities that conventional injection systems lack for hydraulic fracturing. In addition to its ability to generate foam with controlled quality, it is capable of cycling pressure levels between specified values up to frequencies of 50 Hz. The latter capability was developed to evaluate the hypothesis that cyclic loading of samples would produce enhanced fracturing. The system consists of two sections: one for foam generation and another for foam injection. The foam is generated through separate control and pressurization of liquid and gas phases with controlled flow rates. The injection section is equipped with a low-flow Coriolis flow that monitors the density of foam to ensure the injection is in the range of target foam quality2. Experimental results of foam fracturing are reported for cylindrical granite specimens using water and aqueous N2 foam as the fracturing fluids. All experiments were performed for unconfined conditions. The effects of injection mode (i.e., monotonic vs cyclic pressurization) on breakdown pressure and failure response sample were investigated using water alone as a fracturing fluid and foams with a range of compositions. It was found that in the case of monotonic injection, the breakdown pressure of granite specimens tended to be slightly higher when fracturing with foam. Additionally, with a foam quality of 90%, the water use can be reduced by 50 to 84%, depending on hole size. On the other hand, it was observed that the breakdown pressure can be brought down to 70% of the monotonic breakdown pressure by using low cycle fatigue. Finally, discussions are presented regarding injectivity and water use reduction.
15 GEOTHERMAL ENERGY↗
Stochastic projective splitting
Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.
97 MATHEMATICS AND COMPUTING↗
Modeling the effect of wind speed and direction shear on utility‐scale wind turbine power production
Abstract Wind speed and direction variations across the rotor affect power production. As utility‐scale turbines extend higher into the atmospheric boundary layer (ABL) with larger rotor diameters and hub heights, they increasingly encounter more complex wind speed and direction variations. We assess three models for power production that account for wind speed and direction shear. Two are based on actuator disc representations, and the third is a blade element representation. We also evaluate the predictions from a standard power curve model that has no knowledge of wind shear. The predictions from each model, driven by wind profile measurements from a profiling LiDAR, are compared to concurrent power measurements from an adjacent utility‐scale wind turbine. In the field measurements of the utility‐scale turbine, discrete combinations of speed and direction shear induce changes in power production of −19% to +34% relative to the turbine power curve for a given hub height wind speed. Positive speed shear generally corresponds to over‐performance and increasing magnitudes of direction shear to greater under‐performance, relative to the power curve. Overall, the blade element model produces both higher correlation and lower error relative to the other models, but its quantitative accuracy depends on induction and controller sub‐models. To further assess the influence of complex, non‐monotonic wind profiles, we also drive the models with best‐fit power law wind speed profiles and linear wind direction profiles. These idealized inputs produce qualitative and quantitative differences in power predictions from each model, demonstrating that time‐varying, non‐monotonic wind shear affects wind power production.
Energy & Fuels↗
$c$-functions in flows across dimensions
We explore the notion of c-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic c-function and thereby establish a holographic c-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate c-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d N =4 SYM and compactifications of 6d N = (2, 0) theories.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Entanglement Cost for Infinite-Dimensional Physical Systems
We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state ρ ΑΒ with finite quantum entropy on at least one of the subsystems A or B. This generalizes a foundational result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems. The extension to infinite-dimensional systems is nontrivial because the conventional tools for establishing both the direct and converse bounds, i.e., strong typicality, monotonicity, and asymptotic continuity, are no longer directly applicable. To address this problem, we construct a new entanglement dilution protocol for infinite-dimensional states implementable by local operations and a finite amount of one-way classical communication (one-way LOCC), using weak and strong typicality multiple times. We also prove the optimality of this protocol among all protocols, even under infinite-dimensional separable operations, by developing an argument based on alternative forms of monotonicity and asymptotic continuity of the entanglement of formation for infinite-dimensional states. Along the way, we derive a new integral representation for the quantum entropy of infinite-dimensional states, which we believe to be of independent interest. Our results allow us to fully characterize an important operational entanglement measure—the entanglement cost—for all infinite-dimensional physical systems.
Complexity↗
Micromechanics of Fracture Propagation During Multistage Stress Relaxation and Creep in Brittle Rocks
Time-dependent rock deformation caused by the initiation and growth of fractures leads to the weakening of the rock mass. Understanding the fracturing mechanisms involved in the time-dependent behavior in brittle rocks is very important and to achieve this goal, a systematic series of three types of experiments was performed on double-flawed prismatic Barre granite specimens under unconfined compression. The first series aimed to identify the failure mechanism in the short-term failure mode under monotonic loading, the, second series involved multistage relaxation (constant strain) experiments to analyze the damage at different strain levels, and the third series explored the fracture propagation under multistage creep (constant load) experiments. The spatial and temporal evolution of cracking mechanisms were evaluated using the acoustic emission (AE) and two-dimensional digital image correlation (2D-DIC) techniques to observe the whole crack growth process as well as the accumulated inelastic strain at the specified region of interest. Results suggest that in the case of multistage creep experiments, the time to failure was less compared to the multistage relaxation, when loaded above the crack damage threshold (CD) estimated from the monotonic testing. Furthermore, the frequency magnitude distribution of the AE events generated in the three loading conditions followed the Gutenberg Richter model. A relatively lower b-value was obtained for the creep experiments, indicative of high energy AE events and faster crack growth. In addition, the AE and DIC results also revealed high evolution of tensile cracks at-different stages of creep and relaxation compared to shear and mixed-mode cracks.
58 GEOSCIENCES↗
Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network
A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. Further, the trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Testing and modeling of CLT-to-CLT joints made using hardwood dowels and screws with varying spacing
With the increasing popularity of mass timber, utilizing large-diameter wood screws and hardwood dowels can offer an easy and cost-efficient way to join structural elements. However, the existing research on hardwood dowels is limited to single fastener joints under monotonic loading. No research is available on the group effects of joints with multiple hardwood dowels. Here, this paper presents the results of 96 monotonic and cyclic single-shear plane CLT-to-CLT joint tests with hardwood dowels (Red Oak and Yellow Birch, 25.4 mm diameter) and self-tapping wood screws (8 mm diameter) in Grand-Fir CLT, where screws were inserted both perpendicular and at a 45-degree angle to the grain for comparison to hardwood dowels. The study evaluated the mechanical properties of the joints by changing fastener spacing. Mechanical properties such as yielding and peak strength, displacement, elastic and yielding stiffness, and ductility were evaluated. The results showed equal strength and stiffness properties for hardwood dowels comparable with large-diameter screws. Additionally, the hardwood dowel joints demonstrated moderate ductility properties. The strength and stiffness of the tested joints were compared with analytical equations found in the literature by considering the group action factor of the fasteners. Lastly, a nonlinear force-displacement model was presented and compared to the experimental results and analytical calculations, which gives the possibility to predict and optimize the mechanical behavior of hardwood dowel and screw joints with varying numbers and spacing between fasteners.
36 MATERIALS SCIENCE↗