Causal understanding is important in many disciplines of science and engineering, where we seek to understand how different factors in the system causally affect an experiment or situation and pave a pathway towards creating effective or optimising existing models. Examples of use cases are autonomous exploration and modelling of unknown environments or assessing key variables in optimising large complex systems. In this paper, we analyse a Reinforcement Learning approach called Causal Curiosity, which aims to estimate as accurately and efficiently as possible, without directly measuring them, the value of factors that causally determine the dynamics of a system. Whilst the idea presents a pathway forward, measurement accuracy is the foundation of methodology effectiveness. Focusing on the current causal curiosity's robotic manipulator, we present for the first time a measurement accuracy analysis of the future potentials and current limitations of this technique and an analysis of its sensitivity and confounding factor disentanglement capability - crucial for causal analysis. As a result of our work, we promote proposals for an improved and efficient design of Causal Curiosity methods to be applied to real-world complex scenarios.
Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some work has been done to quantify the different uncertainties that arise when dealing with PINNs. In this paper, we use a two-step procedure to train Bayesian Neural Networks that provide uncertainties over the solutions to differential equation systems provided by PINNs. We use available error bounds over PINNs to formulate a heteroscedastic variance that improves the uncertainty estimation. Furthermore, we solve forward problems and utilize the obtained uncertainties when doing parameter estimation in inverse problems in cosmology.
Multimodal learning is an emerging research topic across multiple disciplines but has rarely been applied to planetary science. In this contribution, we identify that reflectance parameter estimation and image-based 3D reconstruction of lunar images can be formulated as a multimodal learning problem. We propose a single, unified transformer architecture trained to learn shared representations between multiple sources like grayscale images, digital elevation models, surface normals, and albedo maps. The architecture supports flexible translation from any input modality to any target modality. Predicting DEMs and albedo maps from grayscale images simultaneously solves the task of 3D reconstruction of planetary surfaces and disentangles photometric parameters and height information. Our results demonstrate that our foundation model learns physically plausible relations across these four modalities. Adding more input modalities in the future will enable tasks such as photometric normalization and co-registration.
As Large Language Models (LLMs) and other AI systems evolve, robustly estimating their capabilities from inherently stochastic outputs while systematically quantifying uncertainty in these estimates becomes increasingly important. Further, advanced AI evaluations often have a nested hierarchical structure, exhibit high levels of complexity, and come with high costs in testing the most advanced AI systems. To address these challenges, we introduce HiBayES, a generalizable Hierarchical Bayesian modeling framework for AI Evaluation Statistics. HiBayES supports robust inferences in classical question-answer benchmarks and advanced agentic evaluations, particularly in low-data scenarios (e.g., < 20 data points per evaluation). Built on Generalized Linear Models (GLMs), Bayesian data analysis, and formal model comparison, HiBayES provides principled uncertainty quantification and robust parameter estimation. This paper offers a comprehensive introduction to HiBayES, including illustrative examples, comparisons to conventional statistical methods, and practical guidance for implementing multilevel Bayesian GLMs. Additionally, we provide a HiBayES software package [4] (Beta version) for out-of-the-box implementation.
Cellular response to environmental and internal signals can be modeled by dynamical gene regulatory networks (GRN). In the literature, three main classes of gene network models can be distinguished: (i) non-quantitative (or data-based) models which do not describe the probability distribution of gene expressions; (ii) quantitative models which fully describe the probability distribution of all genes coexpression; and (iii) mechanistic models which allow for a causal interpretation of gene interactions. We propose two rigorous frameworks to model gene alteration in a dynamical GRN, depending on whether the network model is quantitative or mechanistic. We explain how these models can be used for design of experiment, or, if additional alteration data are available, for validation purposes or to improve the parameter estimation of the original model. We apply these methods to the Gaussian graphical model, which is quantitative but non-mechanistic, and to mechanistic models of Bayesian networks and penalized linear regression.
Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood Estimation (MLE), Kalman Filtering, Inverse Variable Method, and more have historically been used to estimate the parameters of stochastic differential equations, the recent explosion of deep learning technology suggests that models such as a Recurrent Neural Network (RNN) could produce more precise estimators. We present a series of experiments that compare the estimation accuracy and computational expensiveness of a statistical method (MLE) with a deep learning model (RNN) for the parameters of the Ornstein-Uhlenbeck process.
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint via Lagrangian relaxation, transforming it into a regularization term in the objective function. A particularly challenging class includes the zero-norm function, which promotes sparsity in statistical parameter estimation. Most existing exact methods for solving these problems introduce binary variables and artificial bounds to reformulate them as higher-dimensional mixed-integer programs, solvable by standard solvers. Other exact approaches exploit specific structural properties of the objective, making them difficult to generalize across different problem types. Alternative methods employ nonconvex penalties with favorable statistical characteristics, but these are typically addressed using heuristic or local optimization techniques due to their structural complexity. In this paper, we propose a novel graph-based method to globally solve optimization problems involving generalized norm-bounding constraints. Our approach encompasses standard $\ell_p$-norms for $p \in [0, \infty)$ and nonconvex penalties such as SCAD and MCP. We leverage decision diagrams to construct strong convex relaxations directly in the original variable space, eliminating the need for auxiliary variables or artificial bounds. Integrated into a spatial branch-and-cut framework, our method guarantees convergence to the global optimum. We demonstrate its effectiveness through preliminary computational experiments on benchmark sparse linear regression problems involving complex nonconvex penalties, which are not tractable using existing global optimization techniques.
We propose a novel pilot-free multi-user uplink framework for integrated sensing and communication (ISAC) in mm-wave networks, where single-antenna users transmit orthogonal frequency division multiplexing signals without dedicated pilots. The base station exploits the spatial and velocity diversities of users to simultaneously decode messages and detect targets, transforming user transmissions into a powerful sensing tool. Each user's signal, structured by a known codebook, propagates through a sparse multi-path channel with shared moving targets and user-specific scatterers. Notably, common targets induce distinct delay-Doppler-angle signatures, while stationary scatterers cluster in parameter space. We formulate the joint multi-path parameter estimation and data decoding as a 3D super-resolution problem, extracting delays, Doppler shifts, and angles-of-arrival via atomic norm minimization, efficiently solved using semidefinite programming. A core innovation is multiuser fusion, where diverse user observations are collaboratively combined to enhance sensing and decoding. This approach improves robustness and integrates multi-user perspectives into a unified estimation framework, enabling high-resolution sensing and reliable communication. Numerical results show that the proposed framework significantly enhances both target estimation and communication performance, highlighting its potential for next-generation ISAC systems.
Adaptive radar waveform design grounded in information-theoretic principles is critical for advancing cognitive radar performance in complex environments. This paper investigates the optimization of phase-coded waveforms under constant modulus constraints to jointly enhance target detection and parameter estimation. We introduce a unified design framework based on maximizing a Mutual Information Upper Bound (MIUB), which inherently reconciles the trade-off between detection sensitivity and estimation precision without relying on ad hoc weighting schemes. To model realistic, potentially non-Gaussian statistics of target returns and clutter, we adopt Gaussian Mixture Distributions (GMDs), enabling analytically tractable approximations of the MIUB's constituent Kullback-Leibler divergence and mutual information terms. To address the resulting non-convex problem, we propose the Phase-Coded Dream Optimization Algorithm (PC-DOA), a tailored metaheuristic that leverages hybrid initialization and adaptive exploration-exploitation mechanisms specifically designed for phase-variable optimization. Numerical simulations demonstrate the effectiveness of the proposed method in achieving modestly better detection-estimation trade-off.
We consider stacked intelligent metasurfaces (SIMs) as a tool to improve the performance of bistatic integrated sensing and communications (ISAC) schemes. To that end, we optimize the SIMs and design a radar parameter estimation (RPE) scheme aimed at enhancing radar sensing capabilities as well as communication performance under ISAC-enabling waveforms known to perform well in doubly-dispersive (DD) channels. The SIM optimization is done via a min-max problem formulation solved via steepest ascent with closed-form gradients, while the RPE is carried out via a compressed sensing-based probabilistic data association (PDA) algorithm. Our numerical results indicate that the design of waveforms suitable to mitigating the effects of DD channels is significantly impacted by the emerging SIM technology.
Integrated sensing and communication (ISAC) is one of the key usage scenarios for future sixth-generation (6G) mobile communication networks, where communication and sensing (C&S) services are simultaneously provided through shared wireless spectrum, signal processing modules, hardware, and network infrastructure. Such an integration is strengthened by the technology trends in 6G, such as denser network nodes, larger antenna arrays, wider bandwidths, higher frequency bands, and more efficient utilization of spectrum and hardware resources, which incentivize and empower enhanced sensing capabilities. As the dominant waveform used in contemporary communication systems, orthogonal frequency division multiplexing (OFDM) is still expected to be a very competitive technology for 6G, rendering it necessary to thoroughly investigate the potential and challenges of OFDM ISAC. Thus, this paper aims to provide a comprehensive tutorial overview of ISAC systems enabled by large-scale multi-input multi-output (MIMO) and OFDM technologies and to discuss their fundamental principles, advantages, and enabling signal processing methods. To this end, a unified MIMO-OFDM ISAC system model is first introduced, followed by four frameworks for estimating parameters across the spatial, delay, and Doppler domains, including parallel one-domain, sequential one-domain, joint two-domain, and joint three-domain parameter estimation. Next, sensing algorithms and performance analyses are presented in detail for far-field scenarios where uniform plane wave (UPW) propagation is valid, followed by their extensions to near-field scenarios where uniform spherical wave (USW) characteristics need to be considered. Finally, this paper points out open challenges and outlines promising avenues for future research on MIMO-OFDM ISAC.
We address the channel estimation problem in reconfigurable intelligent surface (RIS) aided broadband systems by proposing a dual-structure and multi-dimensional transformations (DS-MDT) algorithm. The proposed approach leverages the dual-structure features of the channel parameters to assist users experiencing weaker channel conditions, thereby enhancing estimation performance. Moreover, given that the channel parameters are distributed across multiple dimensions of the received tensor, the proposed algorithm employs multi-dimensional transformations to effectively isolate and extract distinct parameters. The numerical results demonstrate the proposed algorithm reduces the normalized mean square error (NMSE) by up to 10 dB while maintaining lower complexity compared to state-of-the-art methods.
Cardiac diffusion tensor imaging (DTI) offers unique insights into cardiomyocyte arrangements, bridging the gap between microscopic and macroscopic cardiac function. However, its clinical utility is limited by technical challenges, including a low signal-to-noise ratio, aliasing artefacts, and the need for accurate quantitative fidelity. To address these limitations, we introduce RSFR (Reconstruction, Segmentation, Fusion & Refinement), a novel framework for cardiac diffusion-weighted image reconstruction. RSFR employs a coarse-to-fine strategy, leveraging zero-shot semantic priors via the Segment Anything Model and a robust Vision Mamba-based reconstruction backbone. Our framework integrates semantic features effectively to mitigate artefacts and enhance fidelity, achieving state-of-the-art reconstruction quality and accurate DT parameter estimation under high undersampling rates. Extensive experiments and ablation studies demonstrate the superior performance of RSFR compared to existing methods, highlighting its robustness, scalability, and potential for clinical translation in quantitative cardiac DTI.
Dynamic positron emission tomography (PET) with [$^{18}$F]FDG enables non-invasive quantification of glucose metabolism through kinetic analysis, often modelled by the two-tissue compartment model (TCKM). However, voxel-wise kinetic parameter estimation using conventional methods is computationally intensive and limited by spatial resolution. Deep neural networks (DNNs) offer an alternative but require large training datasets and significant computational resources. To address these limitations, we propose a physiological neural representation based on implicit neural representations (INRs) for personalized kinetic parameter estimation. INRs, which learn continuous functions, allow for efficient, high-resolution parametric imaging with reduced data requirements. Our method also integrates anatomical priors from a 3D CT foundation model to enhance robustness and precision in kinetic modelling. We evaluate our approach on an [$^{18}$F]FDG dynamic PET/CT dataset and compare it to state-of-the-art DNNs. Results demonstrate superior spatial resolution, lower mean-squared error, and improved anatomical consistency, particularly in tumour and highly vascularized regions. Our findings highlight the potential of INRs for personalized, data-efficient tracer kinetic modelling, enabling applications in tumour characterization, segmentation, and prognostic assessment.
Atmospheric turbulence degrades the quality of astronomical observations in ground-based telescopes, leading to distorted and blurry images. Adaptive Optics (AO) systems are designed to counteract these effects, using atmospheric measurements captured by a wavefront sensor to make real-time corrections to the incoming wavefront. The Fried parameter, r0, characterises the strength of atmospheric turbulence and is an essential control parameter for optimising the performance of AO systems and more recently sky profiling for Free Space Optical (FSO) communication channels. In this paper, we develop a novel data-driven approach, adapting machine learning methods from computer vision for Fried parameter estimation from a single Shack-Hartmann or pyramid wavefront sensor image. Using these data-driven methods, we present a detailed simulation-based evaluation of our approach using the open-source COMPASS AO simulation tool to evaluate both the Shack-Hartmann and pyramid wavefront sensors. Our evaluation is over a range of guide star magnitudes, and realistic noise, atmospheric and instrument conditions. Remarkably, we are able to develop a single network-based estimator that is accurate in both open and closed-loop AO configurations. Our method accurately estimates the Fried parameter from a single WFS image directly from AO telemetry to a few millimetres. Our approach is suitable for real time control, exhibiting 0.83ms r0 inference times on retail NVIDIA RTX 3090 GPU hardware, and thereby demonstrating a compelling economic solution for use in real-time instrument control.
Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers limited physical interpretability. The objective of this paper is to develop a real-time parameter estimation algorithm aimed at identifying time-varying dynamics within an interpretable model structure. An additive model structure is adopted for this purpose, which offers enhanced parsimony and is shown to be particularly suitable for mechanical systems. The proposed approach integrates the recursive simplified refined instrumental variable method with block-coordinate descent to minimize an exponentially-weighted output error cost function. This novel recursive identification method delivers parametric continuous-time additive models and is applicable in both open-loop and closed-loop controlled systems. Its efficacy is shown using numerical simulations and is further validated using experimental data to detect the time-varying resonance dynamics of a flexible beam system. These results demonstrate the effectiveness of the proposed approach for online and interpretable estimation for advanced monitoring and control applications.
Biosignal monitoring, in particular heart activity through heart rate (HR) and heart rate variability (HRV) tracking, is vital in enabling continuous, non-invasive tracking of physiological and cognitive states. Recent studies have explored compact, head-worn devices for HR and HRV monitoring to improve usability and reduce stigma. However, this approach is challenged by the current reliance on wet electrodes, which limits usability, the weakness of ear-derived signals, making HR/HRV extraction more complex, and the incompatibility of current algorithms for embedded deployment. This work introduces a single-ear wearable system for real-time ECG (Electrocardiogram) parameter estimation, which directly runs on BioGAP, an energy-efficient device for biosignal acquisition and processing. By combining SoA in-ear electrode technology, an optimized DeepMF algorithm, and BioGAP, our proposed subject-independent approach allows for robust extraction of HR/HRV parameters directly on the device with just 36.7 uJ/inference at comparable performance with respect to the current state-of-the-art architecture, achieving 0.49 bpm and 25.82 ms for HR/HRV mean errors, respectively and an estimated battery life of 36h with a total system power consumption of 7.6 mW. Clinical relevance: The ability to reconstruct ECG signals and extract HR and HRV paves the way for continuous, unobtrusive cardiovascular monitoring with head-worn devices. In particular, the integration of cardiovascular measurements in everyday-use devices (such as earbuds) has potential in continuous at-home monitoring to enable early detection of cardiovascular irregularities.
L\'evy processes are widely used in financial modeling due to their ability to capture discontinuities and heavy tails, which are common in high-frequency asset return data. However, parameter estimation remains a challenge when associated likelihoods are unavailable or costly to compute. We propose a fast and accurate method for L\'evy parameter estimation using the neural Bayes estimation (NBE) framework -- a simulation-based, likelihood-free approach that leverages permutation-invariant neural networks to approximate Bayes estimators. Through extensive simulations across several L\'evy models, we show that NBE outperforms traditional methods in both accuracy and runtime, while also enabling rapid bootstrap-based uncertainty quantification. We illustrate our approach on a challenging high-frequency cryptocurrency return dataset, where the method captures evolving parameter dynamics and delivers reliable and interpretable inference at a fraction of the computational cost of traditional methods. NBE provides a scalable and practical solution for inference in complex financial models, enabling parameter estimation and uncertainty quantification over an entire year of data in just seconds. We additionally investigate nearly a decade of high-frequency Bitcoin returns, requiring less than one minute to estimate parameters under the proposed approach.
In this paper, we address the problem of a two-player linear quadratic differential game with incomplete information, a scenario commonly encountered in multi-agent control, human-robot interaction (HRI), and approximation methods for solving general-sum differential games. While solutions to such linear differential games are typically obtained through coupled Riccati equations, the complexity increases when agents have incomplete information, particularly when neither is aware of the other's cost function. To tackle this challenge, we propose a model-based Peer-Aware Cost Estimation (PACE) framework for learning the cost parameters of the other agent. In PACE, each agent treats its peer as a learning agent rather than a stationary optimal agent, models their learning dynamics, and leverages this dynamic to infer the cost function parameters of the other agent. This approach enables agents to infer each other's objective function in real time based solely on their previous state observations and dynamically adapt their control policies. Furthermore, we provide a theoretical guarantee for the convergence of parameter estimation and the stability of system states in PACE. Additionally, in our numerical studies, we demonstrate how modeling the learning dynamics of the other agent benefits PACE, compared to approaches that approximate the other agent as having complete information, particularly in terms of stability and convergence speed.
Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process effectively, especially in the presence of spatial heterogeneity and heavy-tailed marginal distributions. To overcome this issue, we present a spatial autoregressive modeling framework, which maps observations at a location and its neighbors to independent random variables. This is a highly flexible modeling approach and well-suited for non-Gaussian fields, providing simpler interpretability. In particular, we consider the SAR model with Generalized Extreme Value distribution innovations to combine the observation at a central grid location with its neighbors, capturing extreme spatial behavior based on the heavy-tailed innovations. While these models are fast to simulate by exploiting the sparsity of the key matrices in the computations, the maximum likelihood estimation of the parameters is prohibitive due to the intractability of the likelihood, making optimization challenging. To overcome this, we train a convolutional neural network on a large training set that covers a useful parameter space, and then use the trained network for fast parameter estimation. Finally, we apply this model to analyze annual maximum precipitation data from ERA-Interim-driven Weather Research and Forecasting (WRF) simulations, allowing us to explore its spatial extreme behavior across North America.