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Results for “Stochastic numerical methods”

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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240 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗
DOE OSTI2024

Differentiable stochastic halo occupation distribution

ABSTRACT In this work, we demonstrate how differentiable stochastic sampling techniques developed in the context of deep reinforcement learning can be used to perform efficient parameter inference over stochastic, simulation-based, forward models. As a particular example, we focus on the problem of estimating parameters of halo occupation distribution (HOD) models that are used to connect galaxies with their dark matter haloes. Using a combination of continuous relaxation and gradient re-parametrization techniques, we can obtain well-defined gradients with respect to HOD parameters through discrete galaxy catalogue realizations. Having access to these gradients allows us to leverage efficient sampling schemes, such as Hamiltonian Monte Carlo, and greatly speed up parameter inference. We demonstrate our technique on a mock galaxy catalogue generated from the Bolshoi simulation using a standard HOD model and find near-identical posteriors as standard Markov chain Monte Carlo techniques with an increase of ∼8× in convergence efficiency. Our differentiable HOD model also has broad applications in full forward model approaches to cosmic structure and cosmological analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dynamics retrieval from stochastically weighted incomplete data by low-pass spectral analysis

Time-resolved serial femtosecond crystallography (TR-SFX) provides access to protein dynamics on sub-picosecond timescales, and with atomic resolution. Due to the nature of the experiment, these datasets are often highly incomplete and the measured diffracted intensities are affected by partiality. To tackle these issues, one established procedure is that of splitting the data into time bins, and averaging the multiple measurements of equivalent reflections within each bin. This binning and averaging often involve a loss of information. Here, we propose an alternative approach, which we call low-pass spectral analysis (LPSA). In this method, the data are projected onto the subspace defined by a set of trigonometric functions, with frequencies up to a certain cutoff. This approach attenuates undesirable high-frequency features and facilitates retrieving the underlying dynamics. A time-lagged embedding step can be included prior to subspace projection to improve the stability of the results with respect to the parameters involved. Subsequent modal decomposition allows to produce a low-rank description of the system's evolution. Using a synthetic time-evolving model with incomplete and partial observations, we analyze the LPSA results in terms of quality of the retrieved signal, as a function of the parameters involved. We compare the performance of LPSA to that of a range of other sophisticated data analysis techniques. We show that LPSA allows to achieve excellent dynamics reconstruction at modest computational cost. Finally, we demonstrate the superiority of dynamics retrieval by LPSA compared to time binning and merging, which is, to date, the most commonly used method to extract dynamical information from TR-SFX data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

An indirect approach to optimize the reaction rates of thermal NO formation for diesel engines

With stringent emission regulations, it has become more important for modern diesel engine manufacturers to accurately predict engine-out nitrogen oxide (NO x ) emissions across a wide range of operating conditions. Thermal NO is the major source of engine-out NO x in modern diesel engines. For thermal NO formation, several earlier studies have recommended the forward and reverse reaction rate coefficients of the rate-limiting reaction (O + N 2 ⇌ NO + N). However, due to deficiencies in sub-models and inadequacies of reduced chemical mechanisms to represent diesel combustion, these recommended values more often than not need to be adjusted in reduced order combustion models to accurately predict engine-out NO x . Hence, in this work a systematic and computationally efficient approach has been proposed to streamline the process of determining the optimum reaction rate coefficients. Here, to develop the optimization approach, four different production diesel engines with different operating conditions in terms of speed, load, and exhaust-gas recirculation have been considered. Numerical simulations have been performed using a detailed zero-dimensional velocity-composition-frequency transported probability density function (0D-VCF-tPDF) model that uses hundreds of notional particles to capture in-cylinder stratification. Four different combinations of hydrocarbon and NO x chemical mechanisms were used to represent chemistry. It was found that for the rate-limiting reaction, the pre-exponent factors (A f1 , A r1 ) and activation energies (E A,f1 , E A,r1 ) of the forward and reverse reaction rates follow a linear band in A f1 - E A,f1 and A r1 - E A,r1 space where predicted engine-out NO x match the measured values closely. By encompassing such bands from different engines and considering constraints on activation energies, a reduced search domain of pre-exponent factors and activation energies was constructed that is expected to be applicable to any diesel engine. Eventually, computationally efficient three-line and one-line search approaches were proposed to determine the optimum values of the pre-exponent factors and activation energies that led to a minimum error between measured and predicted engine-out NO x . Finally, these three-line and one-line NO x optimization approaches were applied to a fifth production diesel engine for which the 0D-VCF-tPDF model showed a very good predictive performance in terms of predicting peak pressure, 50% burn rate, and engine-out NO x when compared to measured and 3D-CFD values.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Innovating the next generation of commercial smart building software

Nearly 30% of commercial building energy use is wasted due to equipment faults and HVAC controls problems. The result is increased emissions, compromised comfort and productivity, and less reliable coordination of building power needs with a clean grid. The energy impact alone represents $17 billion in potential savings. Today’s smart building software provides a robust solution to address these operational deficiencies. Energy management and information systems (EMIS) are saving up to 9% on average, with two-year paybacks. They are being incorporated into energy management processes, commissioning services, and utility programs. As effective as they are, two barriers prevent even deeper benefits; limited personnel to fix problems once they are identified, and the expense and time to manually implement changes in control systems. In partnership with the research community, the EMIS industry is developing new capabilities to overcome these barriers. Moving beyond siloed products for either fault detection and diagnostics, or optimal control, these new capabilities empower users to not only automatically identify faults, but also to push corrective action, and control improvements to their buildings. In this paper, several areas for enhancements are documented: ‘one-time’ correction of faults such as setpoints, schedules, and economizer lockouts; short-term active testing for automated proportional integral derivative (PID) loop tuning and functional testing; and continuous supervisory control for demand flexibility and year-round efficiency. Results are presented from a pair of partner implementations out of a dozen providers integrating these enhancements into their products, including field tests from across the country, and insights into operator acceptance and integration into operations and maintenance practices.

Casillas, Armando↗