We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables representing sensor locations, sampling times, or measurement angles, within a single optimization loop. By optimizing measurement locations directly rather than weighting a dense grid of candidates, the proposed approach enforces sparsity by design, eliminates the need for l1 tuning, and substantially reduces computational complexity. We validate NODE on an analytically tractable exponential growth benchmark, on MNIST image sampling, and illustrate its effectiveness on a real world sparse view X ray CT example. In all cases, NODE outperforms baseline approaches, demonstrating improved reconstruction accuracy and task-specific performance.

Optimal experimental design is a classic topic in statistics, with many well-studied problems, applications, and solutions. The design problem we study is the placement of sensors to monitor spatiotemporal processes, explicitly accounting for the temporal dimension in our modeling and optimization. We observe that recent advancements in computational sciences often yield large datasets based on physics-based simulations, which are rarely leveraged in experimental design. We introduce a novel model-based sensor placement criterion, along with a highly-efficient optimization algorithm, which integrates physics-based simulations and Bayesian experimental design principles to identify sensor networks that "minimize information loss" from simulated data. Our technique relies on sparse variational inference and (separable) Gauss-Markov priors, and thus may adapt many techniques from Bayesian experimental design. We validate our method through a case study monitoring air temperature in Phoenix, Arizona, using state-of-the-art physics-based simulations. Our results show our framework to be superior to random or quasi-random sampling, particularly with a limited number of sensors. We conclude by discussing practical considerations and implications of our framework, including more complex modeling tools and real-world deployments.

Timely and reliable decision-making is vital for flood emergency response, yet it remains severely hindered by limited and imprecise situational awareness due to various budget and data accessibility constraints. Traditional flood management systems often rely on in-situ sensors to calibrate remote sensing-based large-scale flood depth forecasting models, and further take flood depth estimates to optimize flood response decisions. However, these approaches often take fixed, decision task-agnostic strategies to decide where to put in-situ sensors (e.g., maximize overall information gain) and train flood forecasting models (e.g., minimize average forecasting errors), but overlook that systems with the same sensing gain and average forecasting errors may lead to distinct decisions. To address this, we introduce a novel decision-focused framework that strategically selects locations for in-situ sensor placement and optimize spatio-temporal flood forecasting models to optimize downstream flood response decision regrets. Our end-to-end pipeline integrates four components: a contextual scoring network, a differentiable sensor selection module under hard budget constraints, a spatio-temporal flood reconstruction and forecasting model, and a differentiable decision layer tailored to task-specific objectives. Central to our approach is the incorporation of Implicit Maximum Likelihood Estimation (I-MLE) to enable gradient-based learning over discrete sensor configurations, and probabilistic decision heads to enable differentiable approximation to various constrained disaster response tasks.

Learning operators from data is central to scientific machine learning. While DeepONets are widely used for their ability to handle complex domains, they require fixed sensor numbers and locations, lack mechanisms for uncertainty quantification (UQ), and are thus limited in practical applicability . Recent permutation-invariant extensions, such as the V ariable-Input Deep Operator Network (VIDON), relax these sensor constraints but still rely on sufficiently dense observations and cannot capture uncertainties arising from incomplete measurements or from operators with inherent randomness. T o address these challenges, we propose UQ-SONet, a permutation-invariant operator learning framework with built-in UQ. Our model integrates a set transformer embedding to handle sparse and variable sensor locations, and employs a conditional variational autoencoder (cV AE) to approximate the conditional distribution of the solution operator. By minimizing the negative ELBO, UQ-SONet provides principled uncertainty estimation while maintaining predictive accuracy . Numerical experiments on deterministic and stochastic PDEs, including the Navier-Stokes equation, demonstrate the robustness and effectiveness of the proposed framework. Introduction Learning continuous operators or complex systems from scattered data streams has shown promising success in scientific machine learning, which focuses on modeling mappings between infinite-dimensional function spaces. A prominent example is the Fourier Neural Operator (FNO) [1], which parameterizes the integral kernel in Fourier space. While highly effective for problems on domains that can be discretized or efficiently mapped to Cartesian grids, the applicability of FNO to more general settings remains limited [2].

PySensors is a Python package for selecting and placing a sparse set of sensors for reconstruction and classification tasks. In this major update to PySensors, we introduce spatially constrained sensor placement capabilities, allowing users to enforce constraints such as maximum or exact sensor counts in specific regions, incorporate predetermined sensor locations, and maintain minimum distances between sensors. We extend functionality to support custom basis inputs, enabling integration of any data-driven or spectral basis. We also propose a thermodynamic approach that goes beyond a single "optimal" sensor configuration and maps the complete landscape of sensor interactions induced by the training data. This comprehensive view facilitates integration with external selection criteria and enables assessment of sensor replacement impacts. The new optimization technique also accounts for over- and under-sampling of sensors, utilizing a regularized least squares approach for robust reconstruction. Additionally, we incorporate noise-induced uncertainty quantification of the estimation error and provide visual uncertainty heat maps to guide deployment decisions. To highlight these additions, we provide a brief description of the mathematical algorithms and theory underlying these new capabilities. We demonstrate the usage of new features with illustrative code examples and include practical advice for implementation across various application domains. Finally, we outline a roadmap of potential extensions to further enhance the package's functionality and applicability to emerging sensing challenges.

We present a machine learning framework for adaptive source localization in which agents use a structure-preserving digital twin of a coupled hydrodynamic-transport system for real-time trajectory planning and data assimilation. The twin is constructed with conditional neural Whitney forms (CNWF), coupling the numerical guarantees of finite element exterior calculus (FEEC) with transformer-based operator learning. The resulting model preserves discrete conservation, and adapts in real time to streaming sensor data. It employs a conditional attention mechanism to identify: a reduced Whitney-form basis; reduced integral balance equations; and a source field, each compatible with given sensor measurements. The induced reduced-order environmental model retains the stability and consistency of standard finite-element simulation, yielding a physically realizable, regular mapping from sensor data to the source field. We propose a staggered scheme that alternates between evaluating the digital twin and applying Lloyd's algorithm to guide sensor placement, with analysis providing conditions for monotone improvement of a coverage functional. Using the predicted source field as an importance function within an optimal-recovery scheme, we demonstrate recovery of point sources under continuity assumptions, highlighting the role of regularity as a sufficient condition for localization. Experimental comparisons with physics-agnostic transformer architectures show improved accuracy in complex geometries when physical constraints are enforced, indicating that structure preservation provides an effective inductive bias for source identification.

This paper presents an innovative Transformer-based deep learning strategy for optimizing the placement of sensors aiming at structural health monitoring of semiconductor probe cards. Failures in probe cards, including substrate cracks and loosened screws, would critically affect semiconductor manufacturing yield and reliability. Some failure modes could be detected by equipping a probe card with adequate sensors. Frequency response functions from simulated failure scenarios are adopted within a finite element model of a probe card. A comprehensive dataset, enriched by physics-informed scenario expansion and physics-aware statistical data augmentation, is exploited to train a hybrid Convolutional Neural Network and Transformer model. The model achieves high accuracy (99.83%) in classifying the probe card health states (baseline, loose screw, crack) and an excellent crack detection recall (99.73%). Model robustness is confirmed through a rigorous framework of 3 repetitions of 10-fold stratified cross-validation. The attention mechanism also pinpoints critical sensor locations: an analysis of the attention weights offers actionable insights for designing efficient, cost-effective monitoring systems by optimizing sensor configurations. This research highlights the capability of attention-based deep learning to advance proactive maintenance, enhancing operational reliability and yield in semiconductor manufacturing.

Modal testing plays a critical role in structural analysis by providing essential insights into dynamic behaviour across a wide range of engineering industries. In practice, designing an effective modal test campaign involves complex experimental planning, comprising a series of interdependent decisions that significantly influence the final test outcome. Traditional approaches to test design are typically static-focusing only on global tests without accounting for evolving test campaign parameters or the impact of such changes on previously established decisions, such as sensor configurations, which have been found to significantly influence test outcomes. These rigid methodologies often compromise test accuracy and adaptability. To address these limitations, this study introduces an agent-based decision support framework for adaptive sensor placement across dynamically changing modal test environments. The framework formulates the problem using an underspecified partially observable Markov decision process, enabling the training of a generalist reinforcement learning agent through a dual-curriculum learning strategy. A detailed case study on a steel cantilever structure demonstrates the efficacy of the proposed method in optimising sensor locations across frequency segments, validating its robustness and real-world applicability in experimental settings.

Accurate link-level bicycling volume estimation is essential for sustainable urban transportation planning. However, many cities face significant challenges of high data sparsity due to limited bicycling count sensor coverage. To address this issue, we propose INSPIRE-GNN, a novel Reinforcement Learning (RL)-boosted hybrid Graph Neural Network (GNN) framework designed to optimize sensor placement and improve link-level bicycling volume estimation in data-sparse environments. INSPIRE-GNN integrates Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT) with a Deep Q-Network (DQN)-based RL agent, enabling a data-driven strategic selection of sensor locations to maximize estimation performance. Applied to Melbourne's bicycling network, comprising 15,933 road segments with sensor coverage on only 141 road segments (99% sparsity) - INSPIRE-GNN demonstrates significant improvements in volume estimation by strategically selecting additional sensor locations in deployments of 50, 100, 200 and 500 sensors. Our framework outperforms traditional heuristic methods for sensor placement such as betweenness centrality, closeness centrality, observed bicycling activity and random placement, across key metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Furthermore, our experiments benchmark INSPIRE-GNN against standard machine learning and deep learning models in the bicycle volume estimation performance, underscoring its effectiveness. Our proposed framework provides transport planners actionable insights to effectively expand sensor networks, optimize sensor placement and maximize volume estimation accuracy and reliability of bicycling data for informed transportation planning decisions.

Canine gait analysis using wearable inertial sensors is gaining attention in veterinary clinical settings, as it provides valuable insights into a range of mobility impairments. Neurological and orthopedic conditions cannot always be easily distinguished even by experienced clinicians. The current study explored and developed a deep learning approach using inertial sensor readings to assess whether neurological and orthopedic gait could facilitate gait analysis. Our investigation focused on optimizing both performance and generalizability in distinguishing between these gait abnormalities. Variations in sensor configurations, assessment protocols, and enhancements to deep learning model architectures were further suggested. Using a dataset of 29 dogs, our proposed approach achieved 96% accuracy in the multiclass classification task (healthy/orthopedic/neurological) and 82% accuracy in the binary classification task (healthy/non-healthy) when generalizing to unseen dogs. Our results demonstrate the potential of inertial-based deep learning models to serve as a practical and objective diagnostic and clinical aid to differentiate gait assessment in orthopedic and neurological conditions.