This minisymposium is devoted to recent developments in methodologies, applications, and lessons-learned in estimating physical parameters in complex physical systems. Mathematical models of complex real-world processes have been used to model physical processes of interest in science, engineering, medicine, and business. Computer models (or simulators) often require a set of inputs (some known and specified, others unknown) to generate predictions for physical processes of interest. Physical observations and simulator output allow us to infer both the unknown inputs and the physical process.
Inference about the physical process in the presence of the high-volume output and model uncertainty is challenging, since appropriate uncertainty assessment is the key success to understand the physical process of interest. In the calibration context, the discrepancy between reality and simulators are difficulty to model. In the inverse problem setting, the high-dimensional input space can make the Bayesian inverse computationally challenging.
Bringing selected leading researchers, this minisymposium has been broken into two sessions: calibration (Part I) and inverse problem (Part II). It includes speakers from Europe and North America and is diverse in experience level from fresh PhD graduates to mid-career researchers with backgrounds in statistics, applied mathematics, and engineering. We hope this minisymposium will serve as a nexus to exchange ideas to address this UQ problem.
16:30
- MOVED FROM CT01 - Likelihood Free SAMC
Kieran Richards | Durham University | United Kingdom
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Kieran Richards | Durham University | United Kingdom
Georgios Karagiannis | Durham University | United Kingdom
Richard Everitt | University of Warwick | United Kingdom
Guang Lin | Purdue University | United States
Approximate Bayesian Computation (ABC) has become a valuable tool for Bayesian Uncertainty Quantification, as it enables inference to be made even when the likelihood is intractable. ABC methods can produce unreliable inference when they introduce high approximation bias into the posterior through careless specification of the ABC kernel. Additionally MCMC-ABC methods often suffer from the local trapping problem which causes poor mixing when the tolerance parameter is low. We introduce a new ABC algorithm, the Stochastic Approximation Monte Carlo ABC (SAMC-ABC), which enabling Bayesian Uncertainty Quantification in increasingly complex systems where inference was previously unreliable. SAMC-ABC adaptively constructs the so called ABC kernel, both reducing the approximation bias and providing immunity to the local trapping problem. We demonstrate the performance of the proposed algorithm with some benchmark examples and find that the method outperforms its competitors. We use our algorithm to analyse a computer model which describes the transmission of the Ebola virus against data from the 2014-15 Ebola outbreak in Liberia.
17:00
Replication or exploration? Active learning and inversion for stochastic simulation experiments
Robert Gramacy | Virginia Tech | United States
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Robert Gramacy | Virginia Tech | United States
We investigate the merits of replication, and provide methods that search for optimal designs (including replicates), in the context of noisy computer simulation experiments. We first show that replication offers the potential to be beneficial from both design and computational perspectives, in the context of Gaussian process surrogate modeling. We then develop a lookahead based sequential design scheme that can determine if a new run should be at an existing input location (i.e., replicate) or at a new one (explore). When paired with a newly developed heteroskedastic Gaussian process model, our dynamic design scheme facilitates learning of signal and noise relationships which can vary throughout the input space. We show that it does so efficiently, on both computational and statistical grounds. In addition to illustrative synthetic examples, we demonstrate performance in a challenging inverse problem setting.
17:30
- MOVED FROM CT01 - Detecting jumps in a jump-discontinuous random field using deep neural networks
Babak Maboudi Afkham | Stuttgart University | Germany
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Babak Maboudi Afkham | Stuttgart University | Germany
Andrea Barth | Stuttgart University | Germany
Random fields are important tools in mathematical modeling which help us include our lack of knowledge or our faulty measurements into scientific computing. Such fields appear frequently as parameters in many modern physics and engineering applications. When these fields are not continuous, statistical analysis and approximation of these models become more involved. In this talk, we investigate detecting jump-discontinuities in the diffusion-coefficient of an elliptic stochastic partial differential equation. This is formulated as an inverse problem. We take a Bayesian approach to formulate the distribution of the jumps in the random field. We then use a Markov chain Monte Carlo (MCMC) method to explore this distribution. Common MCMC methods provide a slow convergence rate which makes solving the forward problem inefficient. In this report, we propose replacing the forward model with a feed-forward fully-connected deep neural network. This dramatically reduces computational costs while providing an accurate forward model estimation. The accuracy and the performance of the method, as well as the implication of using a neural network as a surrogate model, will be discussed.
18:00
Efficient Bayesian inversion for UQ for high dimensional inverse problems
Pranjal Pranjal | Virginia Tech | United States
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Pranjal Pranjal | Virginia Tech | United States
Solving real-world partial differential equations (PDE) based inverse problems with many measurements can be computationally expensive: each evaluation of the associated (nonlinear) objective function and its derivatives requires solving many large-scale discretized PDEs. In this talk, I will discuss some sampling strategies for obtaining better UQ information for high dimensional distributions that are far from Gaussian and present a pseudo-marginal MCMC approach to reduce the tremendous computational cost associated with such problems. We demonstrate our approach with parameterized Diffuse Optical Tomography as the model problem for Bayesian inversion with a highly nonlinear likelihood function.