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.

Department of Engineering Sciences, University of Agder, NorwayAbstract: Compressed sensing enables sparse sampling but relies on generic bases and random measurements, limiting efficiency and reconstruction quality. Optimal sensor placement uses historcal data to design tailored sampling patterns, yet its fixed, linear bases cannot adapt to nonlinear or sample-specific variations. Generative model-based compressed sensing improves reconstruction using deep generative priors but still employs suboptimal random sampling. We propose an adaptive sparse sensing framework that couples a variational autoencoder prior with reinforcement learning to select measurements sequentially. Experiments show that this approach outperforms CS, OSP, and Generative model-based reconstruction from sparse measurements.

In many scientific and engineering fields, where acquiring high-quality data is expensive--such as medical imaging, environmental monitoring, and remote sensing--strategic sampling of unobserved regions based on prior observations is crucial for maximizing discovery rates within a constrained budget. The rise of powerful generative models, such as diffusion models, has enabled active target discovery in partially observable environments by leveraging learned priors--probabilistic representations that capture underlying structure from data. With guidance from sequentially gathered task-specific observations, these models can progressively refine exploration and efficiently direct queries toward promising regions. However, in domains where learning a strong prior is infeasible due to extremely limited data or high sampling cost (such as rare species discovery, diagnostics for emerging diseases, etc.), these methods struggle to generalize. To overcome this limitation, we propose a novel approach that enables effective active target discovery even in settings with uninformative priors, ensuring robust exploration and adaptability in complex real-world scenarios. Our framework is theoretically principled and draws inspiration from neuroscience to guide its design. Unlike black-box policies, our approach is inherently interpretable, providing clear insights into decision-making. Furthermore, it guarantees a strong, monotonic improvement in prior estimates with each new observation, leading to increasingly accurate sampling and reinforcing both reliability and adaptability in dynamic settings. Through comprehensive experiments and ablation studies across various domains, including species distribution modeling and remote sensing, we demonstrate that our method substantially outperforms baseline approaches.

In various scientific and engineering domains, where data acquisition is costly, such as in medical imaging, environmental monitoring, or remote sensing, strategic sampling from unobserved regions, guided by prior observations, is essential to maximize target discovery within a limited sampling budget. In this work, we introduce Diffusion-guided Active Target Discovery (DiffATD), a novel method that leverages diffusion dynamics for active target discovery. DiffATD maintains a belief distribution over each unobserved state in the environment, using this distribution to dynamically balance exploration-exploitation. Exploration reduces uncertainty by sampling regions with the highest expected entropy, while exploitation targets areas with the highest likelihood of discovering the target, indicated by the belief distribution and an incrementally trained reward model designed to learn the characteristics of the target. DiffATD enables efficient target discovery in a partially observable environment within a fixed sampling budget, all without relying on any prior supervised training. Furthermore, DiffATD offers interpretability, unlike existing black-box policies that require extensive supervised training. Through extensive experiments and ablation studies across diverse domains, including medical imaging and remote sensing, we show that DiffATD performs significantly better than baselines and competitively with supervised methods that operate under full environmental observability.

Radio map estimation (RME) involves spatial interpolation of radio measurements to predict metrics such as the received signal strength at locations where no measurements were collected. The most popular estimators nowadays project the measurement locations to a regular grid and complete the resulting measurement tensor with a convolutional deep neural network. Unfortunately, these approaches suffer from poor spatial resolution and require a great number of parameters. The first contribution of this paper addresses these limitations by means of an attention-based estimator named Spatial TransfOrmer for Radio Map estimation (STORM). This scheme not only outperforms the existing estimators, but also exhibits lower computational complexity, translation equivariance, rotation equivariance, and full spatial resolution. The second contribution is an extended transformer architecture that allows STORM to perform active sensing, by which the next measurement location is selected based on the previous measurements. This is particularly useful for minimization of drive tests (MDT) in cellular networks, where operators request user equipment to collect measurements. Finally, STORM is extensively validated by experiments with one ray-tracing and two real-measurement datasets.

This paper introduces a state-machine model for a multi-modal, multi-robot environmental sensing algorithm tailored to dynamic real-world settings. The algorithm uniquely combines two exploration strategies for gas source localization and mapping: (1) an initial exploration phase using multi-robot coverage path planning with variable formations for early gas field indication; and (2) a subsequent active sensing phase employing multi-robot swarms for precise field estimation. The state machine governs the transition between these two phases. During exploration, a coverage path maximizes the visited area while measuring gas concentration and estimating the initial gas field at predefined sample times. In the active sensing phase, mobile robots in a swarm collaborate to select the next measurement point, ensuring coordinated and efficient sensing. System validation involves hardware-in-the-loop experiments and real-time tests with a radio source emulating a gas field. The approach is benchmarked against state-of-the-art single-mode active sensing and gas source localization techniques. Evaluation highlights the multi-modal switching approach's ability to expedite convergence, navigate obstacles in dynamic environments, and significantly enhance gas source location accuracy. The findings show a 43% reduction in turnaround time, a 50% increase in estimation accuracy, and improved robustness of multi-robot environmental sensing in cluttered scenarios without collisions, surpassing the performance of conventional active sensing strategies.

Radio maps quantify magnitudes such as the received signal strength at every location of a geographical region. Although the estimation of radio maps has attracted widespread interest, the vast majority of works rely on simulated data and, therefore, cannot establish the effectiveness and relative performance of existing algorithms in practice. To fill this gap, this paper presents the first comprehensive and rigorous study of radio map estimation (RME) in the real world. The main features of the RME problem are analyzed and the capabilities of existing estimators are compared using large measurement datasets collected in this work. By studying four performance metrics, recent theoretical findings are empirically corroborated and a large number of conclusions are drawn. Remarkably, the estimation error is seen to be reasonably small even with few measurements, which establishes the viability of RME in practice. Besides, from extensive comparisons, it is concluded that estimators based on deep neural networks necessitate large volumes of training data to exhibit a significant advantage over more traditional methods. Combining both types of schemes is seen to result in a novel estimator that features the best performance in most situations. The acquired datasets are made publicly available to enable further studies.

Neutron scattering experiments at three-axes spectrometers (TAS) investigate magnetic and lattice excitations by measuring intensity distributions to understand the origins of materials properties. The high demand and limited availability of beam time for TAS experiments however raise the natural question whether we can improve their efficiency and make better use of the experimenter's time. In fact, there are a number of scientific problems that require searching for signals, which may be time consuming and inefficient if done manually due to measurements in uninformative regions. Here, we describe a probabilistic active learning approach that not only runs autonomously, i.e., without human interference, but can also directly provide locations for informative measurements in a mathematically sound and methodologically robust way by exploiting log-Gaussian processes. Ultimately, the resulting benefits can be demonstrated on a real TAS experiment and a benchmark including numerous different excitations.

Abstract-- We study the sample placement and shortest tour problem for robots tasked with mapping environmental phenomena modeled as stationary random fields. The objective is to minimize the resources used (samples or tour length) while guaranteeing estimation accuracy. We give approximation algorithms for both problems in convex environments. These improve previously known results, both in terms of theoretical guarantees and in simulations. In addition, we disprove an existing claim in the literature on a lower bound for a solution to the sample placement problem.

We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The model is a version of a conditional variational auto-encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty quantification of the prediction. We show that in our model, conditioning on the measurements from the complete flow data leads to a CVAE where only the decoder depends on the measurements. For this reason we call the model as Semi-Conditional Variational Autoencoder (SCVAE). The method, reconstructions and associated uncertainty estimates are illustrated on the velocity data from simulations of 2D flow around a cylinder and bottom currents from the Bergen Ocean Model. The reconstruction errors are compared to those of the Gappy Proper Orthogonal Decomposition (GPOD) method.