4 research outputs found
Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference
Although the no-u-turn sampler (NUTS) is a widely adopted method for
performing Bayesian inference, it requires numerous posterior gradients which
can be expensive to compute in practice. Recently, there has been a significant
interest in physics-based machine learning of dynamical (or Hamiltonian)
systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture.
But these types of architectures have not been applied to solve Bayesian
inference problems efficiently. We propose the use of HNNs for performing
Bayesian inference efficiently without requiring numerous posterior gradients.
We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity
and reduced integration errors. We integrate L-HNNs in NUTS and further propose
an online error monitoring scheme to prevent sampling degeneracy in regions
where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with
online error monitoring considering several complex high-dimensional posterior
densities and compare its performance to NUTS
Multifidelity Active Learning for Failure Estimation of TRISO Nuclear Fuel
The Tristructural isotropic (TRISO)-coated particle fuel is a robust nuclear
fuel proposed to be used for multiple modern nuclear technologies. Therefore,
characterizing its safety is vital for the reliable operation of nuclear
technologies. However, the TRISO fuel failure probabilities are small and the
computational model is time consuming to evaluate them using traditional Monte
Carlo-type approaches. In the paper, we present a multifidelity active learning
approach to efficiently estimate small failure probabilities given an expensive
computational model. Active learning suggests the next best training set for
optimal subsequent predictive performance and multifidelity modeling uses
cheaper low-fidelity models to approximate the high-fidelity model output.
After presenting the multifidelity active learning approach, we apply it to
efficiently predict TRISO failure probability and make comparisons to the
reference results
Gaussian Kernel Methods for Seismic Fragility and Risk Assessment of Mid-Rise Buildings
Seismic fragility functions can be evaluated using the cloud analysis method with linear regression which makes three fundamental assumptions about the relation between structural response and seismic intensity: log-linear median relationship, constant standard deviation, and Gaussian distributed errors. While cloud analysis with linear regression is a popular method, the degree to which these individual and compounded assumptions affect the fragility and the risk of mid-rise buildings needs to be systematically studied. This paper conducts such a study considering three building archetypes that make up a bulk of the building stock: RC moment frame, steel moment frame, and wood shear wall. Gaussian kernel methods are employed to capture the data-driven variations in the median structural response and standard deviation and the distributions of residuals with the intensity level. With reference to the Gaussian kernels approach, it is found that while the linear regression assumptions may not affect the fragility functions of lower damage states, this conclusion does not hold for the higher damage states (such as the Complete state). In addition, the effects of linear regression assumptions on the seismic risk are evaluated. For predicting the demand hazard, it is found that the linear regression assumptions can impact the computed risk for larger structural response values. However, for predicting the loss hazard with downtime as the decision variable, linear regression can be considered adequate for all practical purposes