To make its Ultium EV program a success, GM is counting on battery innovations to make the technology simpler and cheaper. As part of that program, the automaker has boosted its investment with Mitra Chem --a company focused on building batteries in the US using iron-based cathodes -- via a new $60 million financing round. "This is a strategic investment that will further help reinforce GM's efforts in EV batteries, accelerate our work on affordable battery chemistries like LMFP and support our efforts to build a US-focused battery supply chain," said GM VP Gil Golan. Mitra Chem is more of a battery development company than a manufacturer. It uses AI to "simulate, synthesize and test thousands of cathode designs monthly, ranging in size from grams to kilograms," the press release states.

The design of data-driven formulations for machine learning and decision-making with good out-of-sample performance is a key challenge. The observation that good in-sample performance does not guarantee good out-of-sample performance is generally known as overfitting. Practical overfitting can typically not be attributed to a single cause but instead is caused by several factors all at once. We consider here three overfitting sources: (i) statistical error as a result of working with finite sample data, (ii) data noise which occurs when the data points are measured only with finite precision, and finally (iii) data misspecification in which a small fraction of all data may be wholly corrupted. We argue that although existing data-driven formulations may be robust against one of these three sources in isolation they do not provide holistic protection against all overfitting sources simultaneously. We design a novel data-driven formulation which does guarantee such holistic protection and is furthermore computationally viable. Our distributionally robust optimization formulation can be interpreted as a novel combination of a Kullback-Leibler and Levy-Prokhorov robust optimization formulation which is novel in its own right. However, we show how in the context of classification and regression problems that several popular regularized and robust formulations reduce to a particular case of our proposed novel formulation. Finally, we apply the proposed HR formulation on a portfolio selection problem with real stock data, and analyze its risk/return tradeoff against several benchmarks formulations. Our experiments show that our novel ambiguity set provides a significantly better risk/return trade-off.

Sequential experimental design to discover interventions that achieve a desired outcome is a key problem in various domains including science, engineering and public policy. When the space of possible interventions is large, making an exhaustive search infeasible, experimental design strategies are needed. In this context, encoding the causal relationships between the variables, and thus the effect of interventions on the system, is critical for identifying desirable interventions more efficiently. Here, we develop a causal active learning strategy to identify interventions that are optimal, as measured by the discrepancy between the post-interventional mean of the distribution and a desired target mean. The approach employs a Bayesian update for the causal model and prioritizes interventions using a carefully designed, causally informed acquisition function. This acquisition function is evaluated in closed form, allowing for fast optimization. The resulting algorithms are theoretically grounded with information-theoretic bounds and provable consistency results for linear causal models with known causal graph. We apply our approach to both synthetic data and single-cell transcriptomic data from Perturb-CITE-seq experiments to identify optimal perturbations that induce a specific cell state transition. The causally informed acquisition function generally outperforms existing criteria allowing for optimal intervention design with fewer but carefully selected samples.

Variational autoencoders (VAEs) are powerful tools for learning latent representations of data used in a wide range of applications. In practice, VAEs usually require multiple training rounds to choose the amount of information the latent variable should retain. This trade-off between the reconstruction error (distortion) and the KL divergence (rate) is typically parameterized by a hyperparameter $\beta$. In this paper, we introduce Multi-Rate VAE (MR-VAE), a computationally efficient framework for learning optimal parameters corresponding to various $\beta$ in a single training run. The key idea is to explicitly formulate a response function that maps $\beta$ to the optimal parameters using hypernetworks. MR-VAEs construct a compact response hypernetwork where the pre-activations are conditionally gated based on $\beta$. We justify the proposed architecture by analyzing linear VAEs and showing that it can represent response functions exactly for linear VAEs. With the learned hypernetwork, MR-VAEs can construct the rate-distortion curve without additional training and can be deployed with significantly less hyperparameter tuning. Empirically, our approach is competitive and often exceeds the performance of multiple $\beta$-VAEs training with minimal computation and memory overheads.

We consider a setting in which one swarm of agents is to service or track a second swarm, and formulate an optimal control problem which trades off between the competing objectives of servicing and motion costs. We consider the continuum limit where large-scale swarms are modeled in terms of their time-varying densities, and where the Wasserstein distance between two densities captures the servicing cost. We show how this non-linear infinite-dimensional optimal control problem is intimately related to the geometry of Wasserstein space, and provide new results in the case of absolutely continuous densities and constant-in-time references. Specifically, we show that optimal swarm trajectories follow Wasserstein geodesics, while the optimal control tradeoff determines the time-schedule of travel along these geodesics. We briefly describe how this solution provides a basis for a model-predictive control scheme for tracking time-varying and real-time reference trajectories as well.

Decision-focused learning (DFL) is an emerging paradigm in machine learning which trains a model to optimize decisions, integrating prediction and optimization in an end-to-end system. This paradigm holds the promise to revolutionize decision-making in many real-world applications which operate under uncertainty, where the estimation of unknown parameters within these decision models often becomes a substantial roadblock. This paper presents a comprehensive review of DFL. It provides an in-depth analysis of the various techniques devised to integrate machine learning and optimization models, introduces a taxonomy of DFL methods distinguished by their unique characteristics, and conducts an extensive empirical evaluation of these methods proposing suitable benchmark dataset and tasks for DFL. Finally, the study provides valuable insights into current and potential future avenues in DFL research.

The proliferation of technologies, such as extended reality (XR), has increased the demand for high-quality three-dimensional (3D) graphical representations. Industrial 3D applications encompass computer-aided design (CAD), finite element analysis (FEA), scanning, and robotics. However, current methods employed for industrial 3D representations suffer from high implementation costs and reliance on manual human input for accurate 3D modeling. To address these challenges, neural radiance fields (NeRFs) have emerged as a promising approach for learning 3D scene representations based on provided training 2D images. Despite a growing interest in NeRFs, their potential applications in various industrial subdomains are still unexplored. In this paper, we deliver a comprehensive examination of NeRF industrial applications while also providing direction for future research endeavors. We also present a series of proof-of-concept experiments that demonstrate the potential of NeRFs in the industrial domain. These experiments include NeRF-based video compression techniques and using NeRFs for 3D motion estimation in the context of collision avoidance. In the video compression experiment, our results show compression savings up to 48\% and 74\% for resolutions of 1920x1080 and 300x168, respectively. The motion estimation experiment used a 3D animation of a robotic arm to train Dynamic-NeRF (D-NeRF) and achieved an average peak signal-to-noise ratio (PSNR) of disparity map with the value of 23 dB and an structural similarity index measure (SSIM) 0.97.

Quantification is a supervised machine learning task, focused on estimating the class prevalence of a dataset rather than labeling its individual observations. We introduce Continuous Sweep, a new parametric binary quantifier inspired by the well-performing Median Sweep. Median Sweep is currently one of the best binary quantifiers, but we have changed this quantifier on three points, namely 1) using parametric class distributions instead of empirical distributions, 2) optimizing decision boundaries instead of applying discrete decision rules, and 3) calculating the mean instead of the median. We derive analytic expressions for the bias and variance of Continuous Sweep under general model assumptions. This is one of the first theoretical contributions in the field of quantification learning. Moreover, these derivations enable us to find the optimal decision boundaries. Finally, our simulation study shows that Continuous Sweep outperforms Median Sweep in a wide range of situations.

Deterministic model predictive control (MPC), while powerful, is often insufficient for effectively controlling autonomous systems in the real-world. Factors such as environmental noise and model error can cause deviations from the expected nominal performance. Robust MPC algorithms aim to bridge this gap between deterministic and uncertain control. However, these methods are often excessively difficult to tune for robustness due to the nonlinear and non-intuitive effects that controller parameters have on performance. To address this challenge, a unifying perspective on differentiable optimization for control is presented, which enables derivation of a general, differentiable tube-based MPC algorithm. The proposed approach facilitates the automatic and real-time tuning of robust controllers in the presence of large uncertainties and disturbances.

Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be hampered by training pathologies, but also oftentimes by poor choices made by users who lack deep learning expertise. In this paper we present a series of best practices that can significantly improve the training efficiency and overall accuracy of PINNs. We also put forth a series of challenging benchmark problems that highlight some of the most prominent difficulties in training PINNs, and present comprehensive and fully reproducible ablation studies that demonstrate how different architecture choices and training strategies affect the test accuracy of the resulting models. We show that the methods and guiding principles put forth in this study lead to state-of-the-art results and provide strong baselines that future studies should use for comparison purposes. To this end, we also release a highly optimized library in JAX that can be used to reproduce all results reported in this paper, enable future research studies, as well as facilitate easy adaptation to new use-case scenarios.