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It is difficult to avoid the formation of polysulfides by traditional chemical methods, and the synthesis of high purity amorphous MoS2 nanomaterials under ambient conditions is still a challenging task. Here we present a new and facile photochemical strategy for the synthesis of amorphous MoS2 nanomaterials, which is achieved by irradiating a mixed solution containing ammonium molybdate, formic acid and sodium sulfide simply with a Xe lamp for 3 min. The mechanism study reveals that the key step in this synthesis is the photolysis of formic acid to produce free radicals which can rapidly reduce Mo6+ to Mo4+, which then combines with S2− to form MoS2 and inhibits the formation of S–S2− by preventing S2− from participating in the reduction reaction. In addition, the results of a series of experiments indicate that the as-prepared amorphous MoS2 features a small particle size, uniform morphology and relatively large specific surface area, and shows excellent performance in the removal of inorganic heavy metal ions (mercury, lead and cadmium ions) and organic pollutants (rhodamine B and tetracycline), catalase catalysis and a lithium battery anode, showing its great potential and broad application prospects in the fields of environmental remediation, clean energy and green catalysis.

It is difficult to avoid the formation of polysulfides by traditional chemical methods, and the synthesis of high purity amorphous MoS

We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion, subsurface flow processes, and rock physics models. For the inverse modeling, we handle the back-propagation of gradients by an intrusive automatic differentiation strategy that offers three levels of user control: (1) at the wave physics level, we adopted the discrete adjoint method in order to use our existing high-performance FWI code; (2) at the rock physics level, we used built-in operators from the $\texttt{TensorFlow}$ backend; (3) at the flow physics level, we implemented customized PDE operators for the potential and nonlinear saturation equations. These three levels of gradient computation strike a good balance between computational efficiency and programming efficiency, and when chained together, constitute a coupled inverse system. We use numerical experiments to demonstrate that (1) the three-level coupled inverse problem is superior in terms of accuracy to a traditional decoupled inversion strategy; (2) it is able to simultaneously invert for parameters in empirical relationships such as the rock physics models; and (3) the inverted model can be used for reservoir performance prediction and reservoir management/optimization purposes.

We present the Cholesky-factored symmetric positive definite neural network (SPD-NN) for modeling constitutive relations in dynamical equations. Instead of directly predicting the stress, the SPD-NN trains a neural network to predict the Cholesky factor of a tangent stiffness matrix, based on which the stress is calculated in the incremental form. As a result of the special structure, SPD-NN weakly imposes convexity on the strain energy function, satisfies time consistency for path-dependent materials, and therefore improves numerical stability, especially when the SPD-NN is used in finite element simulations. Depending on the types of available data, we propose two training methods, namely direct training for strain and stress pairs and indirect training for loads and displacement pairs. We demonstrate the effectiveness of SPD-NN on hyperelastic, elasto-plastic, and multiscale fiber-reinforced plate problems from solid mechanics. The generality and robustness of the SPD-NN make it a promising tool for a wide range of constitutive modeling applications., 31 pages, 20 figures

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately., 44 pages, 13 figures

Full-waveform inversion (FWI) is an accurate imaging approach for modeling the velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We have adopted a neural-network-based full-waveform inversion (NNFWI) method that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, which suppresses noise in the gradients and mitigates local minima. The velocity model generated by neural networks is input to the same partial differential equation (PDE) solvers used in conventional FWI. The gradients of the neural networks and PDEs are calculated using automatic differentiation, which back propagates gradients through the acoustic PDEs and neural network layers to update the weights of the generative neural network. Experiments on 1D velocity models, the Marmousi model, and the 2004 BP model determine that NNFWI can mitigate local minima, especially for imaging high-contrast features such as salt bodies, and it significantly improves the inversion in the presence of noise. Adding dropout layers to the neural network model also allows analyzing the uncertainty of the inversion results through Monte Carlo dropout. NNFWI opens a new pathway to combine deep learning and FWI for exploiting the characteristics of deep neural networks and the high accuracy of PDE solvers. Because NNFWI does not require extra training data and optimization loops, it provides an attractive and straightforward alternative to conventional FWI.

We propose a novel approach to model viscoelasticity materials, where rate-dependent and non-linear constitutive relationships are approximated with deep neural networks . We assume that inputs and outputs of the neural networks are not directly observable, and therefore common training techniques with input–output pairs for the neural networks are inapplicable. To that end, we develop a novel computational approach to both calibrate parametric and learn neural-network-based constitutive relations of viscoelasticity materials from indirect displacement data in the context of multiple-physics systems. We show that limited displacement data holds sufficient information to quantify the viscoelasticity behavior. We formulate the inverse computation – modeling viscoelasticity properties from observed displacement data – as a PDE-constrained optimization problem and minimize the error functional using a gradient-based optimization method. The gradients are computed by a combination of automatic differentiation and implicit function differentiation rules. The effectiveness of our method is demonstrated through numerous benchmark problems in geomechanics and porous media transport.

Inverse problems associated with stochastic models constitute a significant portion of scientific and engineering applications. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumption; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We propose a new method that estimates the unknown distribution by matching the statistical properties between observed and simulated random processes. We leverage the expressive power of neural networks to approximate the unknown distribution and use a discriminative neural network for computing the statistical discrepancies between the observed and simulated random processes. We demonstrated numerically that the proposed methods can estimate both the model parameters and learn complicated unknown distributions.

We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a neural network to represent the unknown constitutive relations, compare the neural networks with piecewise linear functions, radial basis functions, and radial basis function networks, and show that the neural network outperforms the others in certain cases. We analyze the approximation error of the neural networks using a scaling argument. The training and predicting processes in our framework combine the finite element method, automatic differentiation, and neural networks (or other function approximators). Our framework also allows uncertainty quantification in the form of confidence intervals. Numerical examples on a multiscale fiber-reinforced plate problem and a nonlinear rubbery membrane problem from solid mechanics demonstrate the effectiveness of our framework., 40 pages, 21 figures

Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient efficiently; however, its implementation can be time-consuming and difficult. We develop a general seismic inversion framework to calculate gradients using reverse-mode automatic differentiation. The central idea is that adjoint-state methods and reverse-mode automatic differentiation are mathematically equivalent. The mapping between numerical PDE simulation and deep learning allows us to build a seismic inverse modeling library, ADSeismic, based on deep learning frameworks, which supports high performance reverse-mode automatic differentiation on CPUs and GPUs. We demonstrate the performance of ADSeismic on inverse problems related to velocity model estimation, rupture imaging, earthquake location, and source time function retrieval. ADSeismic has the potential to solve a wide variety of inverse modeling applications within a unified framework.

We consider the isogeometric analysis for fractional PDEs involving the fractional Laplacian in two dimensions. An isogeometric collocation method is developed to discretize the fractional Laplacian and applied to the fractional Poisson problem and the time-dependent fractional porous media equation. Numerical studies exhibit monotonous convergence with a rate of $\mathcal{O}(N^{-1})$, where $N$ is the degrees of freedom. A comparison with finite element analysis shows that the method enjoys higher accuracy per degree of freedom and has a better convergence rate. We demonstrate that isogeometric analysis offers a novel and promising computational tool for nonlocal problems., 23 pages, 8 figures

A simple colorimetric sensor array based on red-emitting CdTe QDs and green-colored fluorescein that exhibited RGB-type color change was proposed for visual detection of trace formaldehyde. In the presence of formaldehyde, the red fluorescence from CdTe QDs was quenched while the green fluorescein was inert thus as a reference. Through harvesting the varied quenching efficiency of different ligand-capped CdTe QDs by formaldehyde, a simple sensor array can be constructed for both selective detection of formaldehyde with high sensitivity (LOD of 0.08 ppm) and identification of the existence of potential interference from acetaldehyde. The quenching mechanisms of formaldehyde toward different ligand capped CdTe QDs were studied with fluorescence lifetime, zeta potential, and also theoretical calculations. The results from theoretical calculations were in good agreement with the experimental results. The proposed sensor array was successfully explored for visual analysis of formaldehyde in indoor air samples.

A low-cost, simple, and highly selective analytical method was developed for sensitive visual detection of selenium in human urine both outdoors and at home, by coupling hydride generation with headspace solid-phase extraction using quantum dots (QDs) immobilized on paper. The visible fluorescence from the CdTe QDs immobilized on paper was quenched by H2Se from hydride generation reaction and headspace solid-phase extraction. The potential mechanism was investigated by using X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) as well as Density Functional Theory (DFT). Potential interferences from coexisting ions, particularly Ag(+), Cu(2+), and Zn(2+), were eliminated. The selectivity was significantly increased because the selenium hydride was effectively separated from sample matrices by hydride generation. Moreover, due to the high sampling efficiency of hydride generation and headspace solid phase extraction, the sensitivity and the limit of detection (LOD) were significantly improved compared to conventional methods. A LOD of 0.1 μg L(-1) and a relative standard deviation (RSD, n = 7) of 2.4% at a concentration of 20 μg L(-1) were obtained when using a commercial spectrofluorometer as the detector. Furthermore, a visual assay based on the proposed method was developed for the detection of Se, 5 μg L(-1) of selenium in urine can be discriminated from the blank solution with the naked eye. The proposed method was validated by analysis of certified reference materials and human urine samples with satisfactory results.

Electronic structure calculations were performed at the B3LYP/6-31G level to identify the stationary structures on the potential energy surfaces for the transmetalation of 2-trimethylstannylbuta-1,3-diene with SnCl(4). The reaction pathways were characterized by locating the transition states on the intrinsic reaction coordinate. The calculations showed that the reaction between the reactant and SnCl(4), which generates 1-trichlorostannylbuta-2,3-diene via transmetalation, has a low energy barrier of 78.1 kJ.mol(-)(1). The following isomerization process is the rate-controlling step. It turned out that the isomerization process from 1-trichlorostannylbuta-2,3-diene to 2-trichloro-stannylbuta-1,3-diene via transmetalation with SnCl(4) is more energetically favorable than other possible isomerization processes.