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Abstract Optical spectrometers are essential tools for analysing light‒matter interactions, but conventional spectrometers can be complicated and bulky. Recently, efforts have been made to develop miniaturized spectrometers. However, it is challenging to overcome the trade-off between miniaturizing size and retaining performance. Here, we present a complementary metal oxide semiconductor image sensor-based miniature computational spectrometer using a plasmonic nanoparticles-in-cavity microfilter array. Size-controlled silver nanoparticles are directly printed into cavity-length-varying Fabry‒Pérot microcavities, which leverage strong coupling between the localized surface plasmon resonance of the silver nanoparticles and the Fabry‒Pérot microcavity to regulate the transmission spectra and realize large-scale arrayed spectrum-disparate microfilters. Supported by a machine learning-based training process, the miniature computational spectrometer uses artificial intelligence and was demonstrated to measure visible-light spectra at subnanometre resolution. The high scalability of the technological approaches shown here may facilitate the development of high-performance miniature optical spectrometers for extensive applications. 

Abstract Lattice thermal conductivity is important for many applications, but experimental measurements or first principles calculations including three-phonon and four-phonon scattering are expensive or even unaffordable. Machine learning approaches that can achieve similar accuracy have been a long-standing open question. Despite recent progress, machine learning models using structural information as descriptors fall short of experimental or first principles accuracy. This study presents a machine learning approach that predicts phonon scattering rates and thermal conductivity with experimental and first principles accuracy. The success of our approach is enabled by mitigating computational challenges associated with the high skewness of phonon scattering rates and their complex contributions to the total thermal resistance. Transfer learning between different orders of phonon scattering can further improve the model performance. Our surrogates offer up to two orders of magnitude acceleration compared to first principles calculations and would enable large-scale thermal transport informatics. 

Abstract In this paper, we propose a new framework to construct confidence sets for a $$d$$-dimensional unknown sparse parameter $${\boldsymbol \theta }$$ under the normal mean model $${\boldsymbol X}\sim N({\boldsymbol \theta },\sigma ^{2}\bf{I})$$. A key feature of the proposed confidence set is its capability to account for the sparsity of $${\boldsymbol \theta }$$, thus named as sparse confidence set. This is in sharp contrast with the classical methods, such as the Bonferroni confidence intervals and other resampling-based procedures, where the sparsity of $${\boldsymbol \theta }$$ is often ignored. Specifically, we require the desired sparse confidence set to satisfy the following two conditions: (i) uniformly over the parameter space, the coverage probability for $${\boldsymbol \theta }$$ is above a pre-specified level; (ii) there exists a random subset $$S$$ of $$\{1,...,d\}$$ such that $$S$$ guarantees the pre-specified true negative rate for detecting non-zero $$\theta _{j}$$’s. To exploit the sparsity of $${\boldsymbol \theta }$$, we allow the confidence interval for $$\theta _{j}$$ to degenerate to a single point 0 for any $$j\notin S$$. Under this new framework, we first consider whether there exist sparse confidence sets that satisfy the above two conditions. To address this question, we establish a non-asymptotic minimax lower bound for the non-coverage probability over a suitable class of sparse confidence sets. The lower bound deciphers the role of sparsity and minimum signal-to-noise ratio (SNR) in the construction of sparse confidence sets. Furthermore, under suitable conditions on the SNR, a two-stage procedure is proposed to construct a sparse confidence set. To evaluate the optimality, the proposed sparse confidence set is shown to attain a minimax lower bound of some properly defined risk function up to a constant factor. Finally, we develop an adaptive procedure to the unknown sparsity. Numerical studies are conducted to verify the theoretical results. 

Abstract With the explosive growth of biomarker data in Alzheimer’s disease (AD) clinical trials, numerous mathematical models have been developed to characterize disease-relevant biomarker trajectories over time. While some of these models are purely empiric, others are causal, built upon various hypotheses of AD pathophysiology, a complex and incompletely understood area of research. One of the most challenging problems in computational causal modeling is using a purely data-driven approach to derive the model’s parameters and the mathematical model itself, without any prior hypothesis bias. In this paper, we develop an innovative data-driven modeling approach to build and parameterize a causal model to characterize the trajectories of AD biomarkers. This approach integrates causal model learning, population parameterization, parameter sensitivity analysis, and personalized prediction. By applying this integrated approach to a large multicenter database of AD biomarkers, the Alzheimer’s Disease Neuroimaging Initiative, several causal models for different AD stages are revealed. In addition, personalized models for each subject are calibrated and provide accurate predictions of future cognitive status. 

Abstract The quantification of microstructural properties to optimize battery design and performance, to maintain product quality, or to track the degradation of LIBs remains expensive and slow when performed through currently used characterization approaches. In this paper, a convolution neural network-based deep learning approach (CNN) is reported to infer electrode microstructural properties from the inexpensive, easy to measure cell voltage versus capacity data. The developed framework combines two CNN models to balance the bias and variance of the overall predictions. As an example application, the method was demonstrated against porous electrode theory-generated voltage versus capacity plots. For the graphite|LiMn$$_2$$ ${}_2$O$$_4$$ ${}_4$chemistry, each voltage curve was parameterized as a function of the cathode microstructure tortuosity and area density, delivering CNN predictions of Bruggeman’s exponent and shape factor with 0.97$$R^2$$ $R^2$score within 2 s each, enabling to distinguish between different types of particle morphologies, anisotropies, and particle alignments. The developed neural network model can readily accelerate the processing-properties-performance and degradation characteristics of the existing and emerging LIB chemistries. 

Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a quadratic behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency.