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1. High-dimensional nonlinear Bayesian inference of poroelastic fields from pressure data

   https://doi.org/10.1177/10812865221140840  

   Karimi, Mina; Massoudi, Mehrdad; Dayal, Kaushik; Pozzi, Matteo (February 2023, Mathematics and Mechanics of Solids)

   We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy measurements. To quantify posterior uncertainty, we adopt Markov Chain Monte Carlo (MCMC) approaches for generating samples. To increase the efficiency of these approaches in high-dimension, we make use of local information about gradient and Hessian of the target potential, also via Hamiltonian Monte Carlo (HMC). Our target application is inferring the field of soil permeability processing observations of pore pressure, using a nonlinear PDE poromechanics model for predicting pressure from permeability. We compare the performance of different sampling approaches in this and other settings. We also investigate the effect of dimensionality and non-gaussianity of distributions on the performance of different sampling methods. 

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2. Sensing and actuation are intricately connected in soft robotics, where contact may change actuator mechanics and robot behavior. To improve soft robotic control and performance, proprioception and contact sensors are needed to report robot state without altering actuation mechanics or introducing bulky, rigid components. For bioinspired McKibben-style fluidic actuators, prior work in sensing has focused on sensing the strain of the actuator by embedding sensors in the actuator bladder during fabrication, or by adhering sensors to the actuator surface after fabrication. However, material property mismatches between sensors and actuators can impede actuator performance, and many soft sensors available for use with fluidic actuators rely on costly or labor-intensive fabrication methods. Here, we demonstrate a low-cost and easy-to manufacture-tubular liquid metal strain sensor for use with soft actuators that can be used to detect actuator strain and contact between the actuator and external objects. The sensor is flexible, can be fabricated with commercial-off-the-shelf components, and can be easily integrated with existing soft actuators to supplement sensing, regardless of actuator shape or size. Furthermore, the soft tubular strain sensor exhibits low hysteresis and high sensitivity. The approach presented in this work provides a low-cost, soft sensing solution for broad application in soft robotics.

   Jackson, Clayton; Chardon, Matthieu; Wang, Y Curtis; Rudi, Johann; Tresch, Matthew; Heckman, Charles J; Quinn, Roger D (August 2023, Springer, Cham.)

   This work explored synaptic strengths in a computational neuroscience model of a controller for the hip joint of a rat which consists of Ia interneurons, Renshaw cells, and the associated motor neurons. This circuit has been referred to as the Canonical Motor Microcircuit (CMM). It is thought that the CMM acts to modulate motor neuron activity at the output stage. We first created a biomechanical model of a rat hindlimb consisting of a pelvis, femur, shin, foot, and flexor-extensor muscle pairs modeled with a Hill muscle model. We then modeled the CMM using non-spiking leaky-integrator neural models connected with conductance-based synapses. To tune the parameters in the network, we implemented an automated approach for parameter search using the Markov chain Monte Carlo (MCMC) method to solve a parameter estimation problem in a Bayesian inference framework. As opposed to traditional optimization techniques, the MCMC method identifies probability densities over the multidimensional space of parameters. This allows us to see a range of likely parameters that produce model outcomes consistent with animal data, determine if the distribution of likely parameters is uni- or multi-modal, as well as evaluate the significance and sensitivity of each parameter. This approach will allow for further analysis of the circuit, specifically, the function and significance of Ia feedback and Renshaw cells. 

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3. Linearized Bayesian inference for Young’s modulus parameter field in an elastic model of slender structures

   https://doi.org/10.1098/rspa.2019.0476  

   Fatehiboroujeni, Soheil; Petra, Noemi; Goyal, Sachin (June 2020, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   The deformations of several slender structures at nano-scale are conceivably sensitive to their non-homogenous elasticity. Owing to their small scale, it is not feasible to discern their elasticity parameter fields accurately using observations from physical experiments. Molecular dynamics simulations can provide an alternative or additional source of data. However, the challenges still lie in developing computationally efficient and robust methods to solve inverse problems to infer the elasticity parameter field from the deformations. In this paper, we formulate an inverse problem governed by a linear elastic model in a Bayesian inference framework. To make the problem tractable, we use a Gaussian approximation of the posterior probability distribution that results from the Bayesian solution of the inverse problem of inferring Young’s modulus parameter fields from available data. The performance of the computational framework is demonstrated using two representative loading scenarios, one involving cantilever bending and the other involving stretching of a helical rod (an intrinsically curved structure). The results show that smoothly varying parameter fields can be reconstructed satisfactorily from noisy data. We also quantify the uncertainty in the inferred parameters and discuss the effect of the quality of the data on the reconstructions. 

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4. Photometric redshift uncertainties in weak gravitational lensing shear analysis: models and marginalization

   https://doi.org/10.1093/mnras/stac3090  

   Zhang, Tianqing; Rau, Markus Michael; Mandelbaum, Rachel; Li, Xiangchong; Moews, Ben (November 2022, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution n(z). Due to the challenge of running Markov chain Monte Carlo (MCMC) in the high-dimensional parameter spaces in which the n(z) uncertainties may be parametrized, it is common practice to simplify the n(z) parametrization or combine MCMC chains that each have a fixed n(z) resampled from the n(z) uncertainties. In this work, we propose a statistically principled Bayesian resampling approach for marginalizing over the n(z) uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalogue, and find that these methods recover statistically consistent error bars for the cosmological parameter constraints for predicted HSC three-year analysis, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for data sets with the constraining power of the full HSC survey data set (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over n(z) uncertainty among the several methods from the literature may modify the 1σ uncertainties on Ωm–S8 constraints by ∼4 per cent, and a careful model selection is needed to ensure credible parameter intervals. 

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5. Bayesian Decision Making in Uncertain MDPs with Large or Infinite-Dimensional Spaces

   Imani, Mandi; Ghoreishi, Seyede; Braga-Neto, Ulisses (December 2018, Advances in Neural Information Processing Systems 31 (NeurIPS’2018))

   We propose a Bayesian decision making framework for control of Markov Decision Processes (MDPs) with unknown dynamics and large, possibly continuous, state, action, and parameter spaces in data-poor environments. Most of the existing adaptive controllers for MDPs with unknown dynamics are based on the reinforcement learning framework and rely on large data sets acquired by sustained direct interaction with the system or via a simulator. This is not feasible in many applications, due to ethical, economic, and physical constraints. The proposed framework addresses the data poverty issue by decomposing the problem into an offline planning stage that does not rely on sustained direct interaction with the system or simulator and an online execution stage. In the offline process, parallel Gaussian process temporal difference (GPTD) learning techniques are employed for near-optimal Bayesian approximation of the expected discounted reward over a sample drawn from the prior distribution of unknown parameters. In the online stage, the action with the maximum expected return with respect to the posterior distribution of the parameters is selected. This is achieved by an approximation of the posterior distribution using a Markov Chain Monte Carlo (MCMC) algorithm, followed by constructing multiple Gaussian processes over the parameter space for efficient prediction of the means of the expected return at the MCMC sample. The effectiveness of the proposed framework is demonstrated using a simple dynamical system model with continuous state and action spaces, as well as a more complex model for a metastatic melanoma gene regulatory network observed through noisy synthetic gene expression data. 

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