In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy that mitigates gradient imbalance through incorporating adaptive weights in conjunction with dynamically adjusting learning rate is used during the training process to improve the convergence of PINNs. The performance of PINNs is assessed here by solving both the forward and inverse problems. In the forward problem, by encapsulating the physical relations among relevant variables, PINNs demonstrate their effectiveness in accurately forecasting the compressor's flow field. PINNs also show obvious advantages over the traditional CFD approaches, particularly in scenarios lacking complete boundary conditions, as is often the case in inverse engineering problems. PINNs successfully reconstruct the flow field of the compressor cascade solely based on partial velocity vectors and near-wall pressure information. Furthermore, PINNs show robust performance in the environment of various levels of aleatory uncertainties stemming from labeled data. This research provides evidence that PINNs can offer turbomachinery designers an additional and promising option alongside the current dominant CFD methods.

Complex distributions of the healthcare expenditure pose challenges to statistical modeling via a single model. Super learning, an ensemble method that combines a range of candidate models, is a promising alternative for cost estimation and has shown benefits over a single model. However, standard approaches to super learning may have poor performance in settings where extreme values are present, such as healthcare expenditure data. We propose a super learner based on the Huber loss, a "robust" loss function that combines squared error loss with absolute loss to down-weight the influence of outliers. We derive oracle inequalities that establish bounds on the finite-sample and asymptotic performance of the method. We show that the proposed method can be used both directly to optimize Huber risk, as well as in finite-sample settings where optimizing mean squared error is the ultimate goal. For this latter scenario, we provide two methods for performing a grid search for values of the robustification parameter indexing the Huber loss. Simulations and real data analysis demonstrate appreciable finite-sample gains in cost prediction and causal effect estimation using our proposed method.

We present a new algorithm for learning unknown governing equations from trajectory data, using and ensemble of neural networks. Given samples of solutions $x(t)$ to an unknown dynamical system $\dot{x}(t)=f(t,x(t))$, we approximate the function $f$ using an ensemble of neural networks. We express the equation in integral form and use Euler method to predict the solution at every successive time step using at each iteration a different neural network as a prior for $f$. This procedure yields M-1 time-independent networks, where M is the number of time steps at which $x(t)$ is observed. Finally, we obtain a single function $f(t,x(t))$ by neural network interpolation. Unlike our earlier work, where we numerically computed the derivatives of data, and used them as target in a Lipschitz regularized neural network to approximate $f$, our new method avoids numerical differentiations, which are unstable in presence of noise. We test the new algorithm on multiple examples both with and without noise in the data. We empirically show that generalization and recovery of the governing equation improve by adding a Lipschitz regularization term in our loss function and that this method improves our previous one especially in presence of noise, when numerical differentiation provides low quality target data. Finally, we compare our results with the method proposed by Raissi, et al. arXiv:1801.01236 (2018) and with SINDy.

Multiple imputation (MI) is the state-of-the-art approach for dealing with missing data arising from non-response in sample surveys. Multiple imputation by chained equations (MICE) is the most widely used MI method, but it lacks theoretical foundation and is computationally intensive. Recently, MI methods based on deep learning models have been developed with encouraging results in small studies. However, there has been limited research on systematically evaluating their performance in realistic settings comparing to MICE, particularly in large-scale surveys. This paper provides a general framework for using simulations based on real survey data and several performance metrics to compare MI methods. We conduct extensive simulation studies based on the American Community Survey data to compare repeated sampling properties of four machine learning based MI methods: MICE with classification trees, MICE with random forests, generative adversarial imputation network, and multiple imputation using denoising autoencoders. We find the deep learning based MI methods dominate MICE in terms of computational time; however, MICE with classification trees consistently outperforms the deep learning MI methods in terms of bias, mean squared error, and coverage under a range of realistic settings.

We provide complete proofs of the lemmas about the properties of the regularized loss function that is used in the second order techniques for learning time-series with structural breaks in Osogami (2021). In addition, we show experimental results that support the validity of the techniques.

Off-policy policy evaluation (OPE) is the problem of estimating the online performance of a policy using only pre-collected historical data generated by another policy. Given the increasing interest in deploying learning-based methods for safety-critical applications, many recent OPE methods have recently been proposed. Due to disparate experimental conditions from recent literature, the relative performance of current OPE methods is not well understood. In this work, we present the first comprehensive empirical analysis of a broad suite of OPE methods. Based on thousands of experiments and detailed empirical analyses, we offer a summarized set of guidelines for effectively using OPE in practice, and suggest directions for future research.

Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed dictionary. Unfortunately, inference in this model involves solving non-smooth optimization problems that are computationally expensive. While significant efforts have focused on developing digital algorithms specifically for this problem, these algorithms are inappropriate for many applications because of the time and power requirements necessary to solve large optimization problems. Based on recent work in computational neuroscience, we explore the potential advantages of continuous time dynamical systems for solving sparse approximation problems if they were implemented in analog VLSI. Specifically, in the simulated task of recovering synthetic and MRI data acquired via compressive sensing techniques, we show that these systems can potentially perform recovery at time scales of 10-20{\mu}s, supporting datarates of 50-100 kHz (orders of magnitude faster that digital algorithms). Furthermore, we show analytically that a wide range of sparse approximation problems can be solved in the same basic architecture, including approximate $\ell^p$ norms, modified $\ell^1$ norms, re-weighted $\ell^1$ and $\ell^2$, the block $\ell^1$ norm and classic Tikhonov regularization.