Mechanics is an important component in the regulation of cell shape, proliferation, migration and differentiation during normal homeostasis and disease states. Biomaterials that match the elastic modulus of soft tissues have been effective for studying this cell mechanobiology, but improvements are needed in order to investigate a wider range of physicochemical properties in a controlled manner. We hypothesized that polydimethylsiloxane (PDMS) blends could be used as the basis of a tunable system where the elastic modulus could be adjusted to match most types of soft tissue. To test this we formulated blends of two commercially available PDMS types, Sylgard 527 and Sylgard 184, which enabled us to fabricate substrates with an elastic modulus anywhere from 5 kPa up to 1.72 MPa. This is a three order-of-magnitude range of tunability, exceeding what is possible with other hydrogel and PDMS systems. Uniquely, the elastic modulus can be controlled independently of other materials properties including surface roughness, surface energy and the ability to functionalize the surface by protein adsorption and microcontact printing. For biological validation, PC12 (neuronal inducible-pheochromocytoma cell line) and C2C12 (muscle cell line) were used to demonstrate that these PDMS formulations support cell attachment and growth and that these substrates can be used to probe the mechanosensitivity of various cellular processes including neurite extension and muscle differentiation.

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Development of Polydimethylsiloxane Substrates with Tunable Elastic Modulus to Study Cell Mechanobiology in Muscle and Nerve

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of dimensionality, the saturation discontinuity due to capillarity effects, and the time-dependence of the multi-output responses. In this paper, we propose a deep convolutional encoder-decoder neural network methodology to tackle these issues. The surrogate modeling task is transformed to an image-to-image regression strategy. This approach extracts high-level coarse features from the high-dimensional input permeability images using an encoder, and then refines the coarse features to provide the output pressure/saturation images through a decoder. A training strategy combining a regression loss and a segmentation loss is proposed in order to better approximate the discontinuous saturation field. To characterize the high-dimensional time-dependent outputs of the dynamic system, time is treated as an additional input to the network that is trained using pairs of input realizations and of the corresponding system outputs at a limited number of time instances. The proposed method is evaluated using a geological carbon storage process-based multiphase flow model with a 2500-dimensional stochastic permeability field. With a relatively small number of training data, the surrogate model is capable of accurately characterizing the spatio-temporal evolution of the pressure and discontinuous CO2 saturation fields and can be used efficiently to compute the statistics of the system responses.

Deep Convolutional Encoder-Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media

Nanoindentation and nanoscratch investigations on graphene-based nanocomposites

Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based surrogate method is developed for the forward model to allow us to solve efficiently such high-dimensional inverse problems. The surrogate is trained using limited evaluations of the forward model. Since the relationship between the time-varying inputs and outputs of the forward transport model is complex, we propose an autoregressive strategy, which treats the output at the previous time step as input to the network for predicting the output at the current time step. We employ a dense convolutional encoder-decoder network architecture in which the high-dimensional input and output fields of the model are treated as images to leverage the robust capability of convolutional networks in image-like data processing. An iterative local updating ensemble smoother (ILUES) algorithm is used as the inversion framework. The proposed method is evaluated using a synthetic contaminant source identification problem with 686 uncertain input parameters. Results indicate that, with relatively limited training data, the deep autoregressive neural network consisting of 27 convolutional layers is capable of providing an accurate approximation for the high-dimensional model input-output relationship. The autoregressive strategy substantially improves the network's accuracy and computational efficiency. The application of the surrogate-based ILUES in solving the inverse problem shows that it can achieve accurate inversion results and predictive uncertainty estimates.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2018WR024638

Deep Autoregressive Neural Networks for High-Dimensional Inverse Problems in Groundwater Contaminant Source Identification

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

Efficient Bayesian experimental design for contaminant source identification

A hybrid model to determine mechanical properties of soft polymers by nanoindentation

Surrogate model based iterative ensemble smoother for subsurface flow data assimilation

[1] In this work, we propose a new collocation method for uncertainty quantification in strongly nonlinear problems. Based on polynomial construction, the traditional probabilistic collocation method (PCM) approximates the model output response, which is a function of the random input parameter, from the Eulerian point of view in specific locations. In some cases, especially when the advection dominates, the model response has a strongly nonlinear profile with a discontinuous shock or large gradient. This nonlinearity in the space domain is then translated to nonlinearity in the random parametric domain, which causes nonphysical oscillation and inaccurate estimation using the traditional PCM. To address this issue, a new location-based transformed probabilistic collocation method (xTPCM) is developed in this study, inspired by the Lagrangian point of view, in which model response is represented by an alternative variable, i.e., the location of a particular response value, which is relatively linear to the random parameter with a smooth profile. The location is then approximated by polynomial construction, from which a sufficient number of location samples are randomly generated and transformed back to obtain the response samples and to estimate the statistical properties. The advantage of the xTPCM is demonstrated through applications to multiphase flow and solute transport in porous media, which shows that the xTPCM achieves higher statistical accuracy than does the PCM, and produces more reasonable realizations without oscillation, while computational effort is greatly reduced compared to the direct sampling Monte Carlo method.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2013WR014055

Probabilistic collocation method for strongly nonlinear problems: 1. Transform by location

Probabilistic collocation method for strongly nonlinear problems: 1. Transform by location: TRANSFORMED PROBABILISTIC COLLOCATION METHOD

Research activities are currently being conducted to study multiphase flow in hydrate-bearing sediments (HBS). In this study, in view of the assumption that hydrates are evenly distributed in HBS with two major hydrate-growth patterns, i.e., pore filling hydrates (PF hydrates), wall coating hydrates (WC hydrates) and a combination of the two, a theoretical relative  permeability model is proposed for gas-water flow through HBS. Besides, in this proposed model, the change in pore structure (e.g., pore radius) of HBS due to effective stress is taken into account. Then, model validation is performed by comparing the predicted results from the derived model with that from the existing model and test data. By setting the value of hydrate saturation to zero, our derived model can be reducible to the existing model, which demonstrates that the existing model is a special case of our model. The results reveal that, under the same saturation, relative permeability to water K rw (or gas K rg ) in PF hydrates is smaller than that in WC hydrates. Moreover, the morphological characteristics of relative permeability curve (relative permeability versus gas saturation) for WC hydrate and PF hydrate are different. Cited as : Lei, G., Liao, Q., Chen, W., Lin, Q., Zhang, L., Xue, L. Stress dependent gas-water relative permeability in gas hydrates: A theoretical model. Advances in Geo-Energy Research, 2020, 4(3): 326-338, doi: 10.46690/ager.2020.03.10

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Qinzhuo Liao

Papers

A hybrid model to determine mechanical properties of soft polymers by nanoindentation

Surrogate model based iterative ensemble smoother for subsurface flow data assimilation

Probabilistic collocation method for strongly nonlinear problems: 1. Transform by location

Probabilistic collocation method for strongly nonlinear problems: 1. Transform by location: TRANSFORMED PROBABILISTIC COLLOCATION METHOD

Stress dependent gas-water relative permeability in gas hydrates: A theoretical model