We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture "partial volumes" and offer a graded interpolation between the widely used A-optimal design and D-optimal design models, obtaining each of them as special cases. We analyze properties of our models, and derive both greedy and convex-relaxation algorithms for computing the associated designs. Our analysis establishes approximation guarantees on these algorithms, while our empirical results substantiate our claims and demonstrate a curious phenomenon concerning our greedy method. Finally, as a byproduct, we obtain new results on the theory of elementary symmetric polynomials that may be of independent interest.

We present BehAV, a novel approach for autonomous robot navigation in outdoor scenes guided by human instructions and leveraging Vision Language Models (VLMs). Our method interprets human commands using a Large Language Model (LLM) and categorizes the instructions into navigation and behavioral guidelines. Navigation guidelines consist of directional commands (e.g., "move forward until") and associated landmarks (e.g., "the building with blue windows"), while behavioral guidelines encompass regulatory actions (e.g., "stay on") and their corresponding objects (e.g., "pavements"). We use VLMs for their zero-shot scene understanding capabilities to estimate landmark locations from RGB images for robot navigation. Further, we introduce a novel scene representation that utilizes VLMs to ground behavioral rules into a behavioral cost map. This cost map encodes the presence of behavioral objects within the scene and assigns costs based on their regulatory actions. The behavioral cost map is integrated with a LiDAR-based occupancy map for navigation. To navigate outdoor scenes while adhering to the instructed behaviors, we present an unconstrained Model Predictive Control (MPC)-based planner that prioritizes both reaching landmarks and following behavioral guidelines. We evaluate the performance of BehAV on a quadruped robot across diverse real-world scenarios, demonstrating a 22.49% improvement in alignment with human-teleoperated actions, as measured by Frechet distance, and achieving a 40% higher navigation success rate compared to state-of-the-art methods.

Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This issue is further amplified in nonlinear and constrained systems that require nesting MPC solvers within iterative procedures. In this paper, we address these issues by developing parallel-in-time algorithms for constrained nonlinear optimization problems that take advantage of massively parallel hardware to achieve logarithmic computational time scaling over the planning horizon. We develop time-parallel second-order solvers based on interior point methods and the alternating direction method of multipliers, leveraging fast convergence and lower computational cost per iteration. The parallelization is based on a reformulation of the subproblems in terms of associative operations that can be parallelized using the associative scan algorithm. We validate our approach on numerical examples of nonlinear and constrained dynamical systems.

Transformers [Vaswani et al., 2017] are versatile models used in various applications, including vision [Yuan et al., 2021, Khan et al., 2022, Dehghani et al., 2023] and natural language processing [Wei et al., 2022b, Touvron et al., 2023]. Their effectiveness in complex tasks is particularly notable in Large Language Models (LLMs) [Wang et al., 2018, Hendrycks et al., 2021], where they excel at generating coherent text and understanding context. This strong performance has led to an increased interest in understanding the Transformer architecture as a computational model capable of executing instructions and solving algorithmic reasoning problems. In this context, Pérez et al. [2021], Wei et al. [2022a] show that Transformers are Turing Complete, and Giannou et al. [2023], Back De Luca and Fountoulakis [2024], Yang et al. [2024] demonstrate that Transformers can effectively encode instructions to solve linear algebra and graphs problems. Additionally, it has been shown that Transformers can perform reasoning tasks using far fewer layers than the number of reasoning steps [Liu et al., 2023], indicating a connection between Transformers and parallel algorithms. To this end, Sanford et al. [2024] further demonstrates that Transformers can simulate the Massively Parallel Computation (MPC) model [Andoni et al., 2018], which is based on the MapReduce framework for large-scale data processing [Dean and Ghemawat, 2008]. Complementing this theoretical framework, empirical studies have demonstrated the capabilities of Transformers, among other models, in executing algorithms [Veličković and Blundell, 2021]. Notable applications include basic arithmetic [Lee et al., 2024], sorting [Tay et al., 2020, Yan et al., 2020], dynamic programming

Regional high-resolution climate projections are crucial for many applications, such as agriculture, hydrology, and natural hazard risk assessment. Dynamical downscaling, the state-of-the-art method to produce localized future climate information, involves running a regional climate model (RCM) driven by an Earth System Model (ESM), but it is too computationally expensive to apply to large climate projection ensembles. We propose a novel approach combining dynamical downscaling with generative artificial intelligence to reduce the cost and improve the uncertainty estimates of downscaled climate projections. In our framework, an RCM dynamically downscales ESM output to an intermediate resolution, followed by a generative diffusion model that further refines the resolution to the target scale. This approach leverages the generalizability of physics-based models and the sampling efficiency of diffusion models, enabling the downscaling of large multi-model ensembles. We evaluate our method against dynamically-downscaled climate projections from the CMIP6 ensemble. Our results demonstrate its ability to provide more accurate uncertainty bounds on future regional climate than alternatives such as dynamical downscaling of smaller ensembles, or traditional empirical statistical downscaling methods. We also show that dynamical-generative downscaling results in significantly lower errors than bias correction and spatial disaggregation (BCSD), and captures more accurately the spectra and multivariate correlations of meteorological fields. These characteristics make the dynamical-generative framework a flexible, accurate, and efficient way to downscale large ensembles of climate projections, currently out of reach for pure dynamical downscaling.

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control strategies must be determined for systems governed by ordinary or stochastic differential equations. Despite its significance, the computational challenges associated with these problems have limited their practical use. To address these limitations, this paper introduces a learning-based approach to DE-constrained optimization that combines techniques from proxy optimization and neural differential equations. The proposed approach uses a dual-network architecture, with one approximating the control strategies, focusing on steady-state constraints, and another solving the associated DEs. This combination enables the approximation of optimal strategies while accounting for dynamic constraints in near real-time. Experiments across problems in energy optimization and finance modeling show that this method provides full compliance with dynamic constraints and it produces results up to 25 times more precise than other methods which do not explicitly model the system's dynamic equations.

Long-Form Question Answering (LFQA) refers to generating in-depth, paragraph-level responses to open-ended questions. Although lots of LFQA methods are developed, evaluating LFQA effectively and efficiently remains challenging due to its high complexity and cost. Therefore, there is no standard benchmark for LFQA evaluation till now. To address this gap, we make the first attempt by proposing a well-constructed, reference-based benchmark named Chinese exAmination for LFQA Evaluation (CALF), aiming to rigorously assess the performance of automatic evaluation metrics for LFQA. The CALF benchmark is derived from Chinese examination questions that have been translated into English. It includes up to 1476 examples consisting of knowledge-intensive and nuanced responses. Our evaluation comprises three different settings to ana lyze the behavior of automatic metrics comprehensively. We conducted extensive experiments on 7 traditional evaluation metrics, 3 prompt-based metrics, and 3 trained evaluation metrics, and tested on agent systems for the LFQA evaluation. The results reveal that none of the current automatic evaluation metrics shows comparable performances with humans, indicating that they cannot capture dense information contained in long-form responses well. In addition, we provide a detailed analysis of the reasons why automatic evaluation metrics fail when evaluating LFQA, offering valuable insights to advance LFQA evaluation systems. Dataset and associated codes can be accessed at our GitHub repository.

A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary differential equation (ODE) models for nonlinear, noisy, and non-autonomous dynamical systems and propose a machine learning method for data-driven system identification. While many methods tackle noisy and limited data, non-stationarity - where differential equation parameters change over time - has received less attention. Our method, dynamic SINDy, combines variational inference with SINDy (sparse identification of nonlinear dynamics) to model time-varying coefficients of sparse ODEs. This framework allows for uncertainty quantification of ODE coefficients, expanding on previous methods for autonomous systems. These coefficients are then interpreted as latent variables and added to the system to obtain an autonomous dynamical model. We validate our approach using synthetic data, including nonlinear oscillators and the Lorenz system, and apply it to neuronal activity data from C. elegans. Dynamic SINDy uncovers a global nonlinear model, showing it can handle real, noisy, and chaotic datasets. We aim to apply our method to a variety of problems, specifically dynamic systems with complex time-dependent parameters.

Neural operators (NOs) have demonstrated remarkable success in learning mappings between function spaces, serving as efficient approximators for the forward solutions of complex physical systems governed by partial differential equations (PDEs). However, while effective as black-box solvers, they offer limited insight into the underlying physical mechanism, due to the lack of interpretable representations of the physical parameters that drive the system. To tackle this challenge, we propose a new paradigm for learning disentangled representations from neural operator parameters, thereby effectively solving an inverse problem. Specifically, we introduce DisentangO, a novel hyper-neural operator architecture designed to unveil and disentangle the latent physical factors of variation embedded within the black-box neural operator parameters. At the core of DisentangO is a multi-task neural operator architecture that distills the varying parameters of the governing PDE through a task-wise adaptive layer, coupled with a hierarchical variational autoencoder that disentangles these variations into identifiable latent factors. By learning these disentangled representations, our model not only enhances physical interpretability but also enables more robust generalization across diverse physical systems. Empirical evaluations across supervised, semi-supervised, and unsupervised learning contexts show that DisentangO effectively extracts meaningful and interpretable latent features, bridging the divide between predictive performance and physical understanding in neural operator frameworks.

Commercial office buildings contribute 17 percent of Carbon Emissions in the US, according to the US Energy Information Administration (EIA), and improving their efficiency will reduce their environmental burden and operating cost. A major contributor of energy consumption in these buildings are the Heating, Ventilation, and Air Conditioning (HVAC) devices. HVAC devices form a complex and interconnected thermodynamic system with the building and outside weather conditions, and current setpoint control policies are not fully optimized for minimizing energy use and carbon emission. Given a suitable training environment, a Reinforcement Learning (RL) agent is able to improve upon these policies, but training such a model, especially in a way that scales to thousands of buildings, presents many practical challenges. Most existing work on applying RL to this important task either makes use of proprietary data, or focuses on expensive and proprietary simulations that may not be grounded in the real world. We present the Smart Buildings Control Suite, the first open source interactive HVAC control dataset extracted from live sensor measurements of devices in real office buildings. The dataset consists of two components: six years of real-world historical data from three buildings, for offline RL, and a lightweight interactive simulator for each of these buildings, calibrated using the historical data, for online and model-based RL. For ease of use, our RL environments are all compatible with the OpenAI gym environment standard. We also demonstrate a novel method of calibrating the simulator, as well as baseline results on training an RL agent on the simulator, predicting real-world data, and training an RL agent directly from data. We believe this benchmark will accelerate progress and collaboration on building optimization and environmental sustainability research.