We present VGGT, a feed-forward neural network that directly infers all key 3D attributes of a scene, including camera parameters, point maps, depth maps, and 3D point tracks, from one, a few, or hundreds of its views. This approach is a step forward in 3D computer vision, where models have typically been constrained to and specialized for single tasks. It is also simple and efficient, reconstructing images in under one second, and still outperforming alternatives that require post-processing with visual geometry optimization techniques. The network achieves state-of-the-art results in multiple 3D tasks, including camera parameter estimation, multi-view depth estimation, dense point cloud reconstruction, and 3D point tracking. We also show that using pretrained VGGT as a feature backbone significantly enhances downstream tasks, such as non-rigid point tracking and feed-forward novel view synthesis. Code and models are publicly available at https://github.com/facebookresearch/vggt.
The recently proposed multi-chirp waveform, affine frequency division multiplexing (AFDM), is regarded as a prospective candidate for integrated sensing and communication (ISAC) due to its robust performance in high-mobility scenarios and full diversity achievement in doubly dispersive channels. However, the insufficient Doppler resolution caused by limited transmission duration can reduce the accuracy of parameter estimation. In this paper, we propose a new off-grid target parameter estimation scheme to jointly estimate the range and velocity of the targets for AFDM-ISAC system, where the off-grid Doppler components are incorporated to enhance estimation accuracy. Specifically, we form the sensing model as an off-grid sparse signal recovery problem relying on the virtual delay and Doppler grids defined in the discrete affine Fourier (DAF) domain, where the off-grid components are regarded as hyper-parameters for estimation. We also employ the expectation-maximization (EM) technique via a sparse Bayesian learning (SBL) framework to update hyper-parameters iteratively. Simulation results indicate that our proposed off-grid algorithm outperforms existing algorithms in sensing performance and is highly robust to the AFDM-ISAC high-mobility scenario.
We design specific neural networks (NNs) for the identification of switching nonlinear systems in the state-space form, which explicitly model the switching behavior and address the inherent coupling between system parameters and switching modes. This coupling is specifically addressed by leveraging the expectation-maximization (EM) framework. In particular, our technique will combine a moving window approach in the E-step to efficiently estimate the switching sequence, together with an extended Kalman filter (EKF) in the M-step to train the NNs with a quadratic convergence rate. Extensive numerical simulations, involving both academic examples and a battery charge management system case study, illustrate that our technique outperforms available ones in terms of parameter estimation accuracy, model fitting, and switching sequence identification.
Alzheimer's disease (AD) is driven by the accumulation of amyloid-beta (Abeta) proteins in the brain, leading to memory loss and cognitive decline. While monoclonal antibodies targeting Abetahave been approved, optimizing their use to maximize benefits while minimizing side effects remains a challenge. This study develops a mathematical model to describe Abeta aggregation, capturing its progression from monomers to toxic oligomers, protofibrils, and fibrils using mass-action kinetics and coarse-grained modeling. The model is calibrated with experimental data, incorporating parameter estimation and sensitivity analysis to ensure accuracy. An optimal control framework is introduced to determine the best drug dosing strategy that reduces toxic Abeta aggregates while minimizing adverse effects, such as amyloid-related imaging abnormalities (ARIA). Results indicate that Donanemab achieves the greatest reduction in fibrils. This work provides a quantitative framework for optimizing AD treatment strategies, offering insights into balancing therapeutic efficacy and safety.
Most of the fundamental, emergent, and phenomenological parameters of particle and nuclear physics are determined through parametric template fits. Simulations are used to populate histograms which are then matched to data. This approach is inherently lossy, since histograms are binned and low-dimensional. Deep learning has enabled unbinned and high-dimensional parameter estimation through neural likelihiood(-ratio) estimation. We compare two approaches for neural simulation-based inference (NSBI): one based on discriminative learning (classification) and one based on generative modeling. These two approaches are directly evaluated on the same datasets, with a similar level of hyperparameter optimization in both cases. In addition to a Gaussian dataset, we study NSBI using a Higgs boson dataset from the FAIR Universe Challenge. We find that both the direct likelihood and likelihood ratio estimation are able to effectively extract parameters with reasonable uncertainties. For the numerical examples and within the set of hyperparameters studied, we found that the likelihood ratio method is more accurate and/or precise. Both methods have a significant spread from the network training and would require ensembling or other mitigation strategies in practice.
An accurate distribution network model is crucial for monitoring, state estimation and energy management. However, existing data-driven methods often struggle with scalability or impose a heavy computational burden on large distribution networks. In this paper, leveraging natural load dynamics, we propose a two-stage line estimation method for multiphase unbalanced distribution networks. Simulation results using real-life load and PV data show that the proposed method reduces computational time by one to two orders of magnitude compared to existing methods.
Active learning aims to efficiently build a labeled training set by strategically selecting samples to query labels from annotators. In this sequential process, each sample acquisition influences subsequent selections, causing dependencies among samples in the labeled set. However, these dependencies are overlooked during the model parameter estimation stage when updating the model using Maximum Likelihood Estimation (MLE), a conventional method that assumes independent and identically distributed (i.i.d.) data. We propose Dependency-aware MLE (DMLE), which corrects MLE within the active learning framework by addressing sample dependencies typically neglected due to the i.i.d. assumption, ensuring consistency with active learning principles in the model parameter estimation process. This improved method achieves superior performance across multiple benchmark datasets, reaching higher performance in earlier cycles compared to conventional MLE. Specifically, we observe average accuracy improvements of 6\%, 8.6\%, and 10.5\% for $k=1$, $k=5$, and $k=10$ respectively, after collecting the first 100 samples, where entropy is the acquisition function and $k$ is the query batch size acquired at every active learning cycle.
We propose a method, funWeightClust, based on a family of parsimonious models for clustering heterogeneous functional linear regression data. These models extend cluster weighted models to functional data, and they allow for multivariate functional responses and predictors. The proposed methodology follows the approach used by the the functional high dimensional data clustering (funHDDC) method. We construct an expectation maximization (EM) algorithm for parameter estimation. Using simulated and benchmark data we show that funWeightClust outperforms funHDDC and several two-steps clustering methods. We also use funWeightClust to analyze traffic patterns in Edmonton, Canada.
Mathematical models of epidemics often use compartmental models dividing the population into several compartments. Based on a microscopic setting describing the temporal evolution of the subpopulation sizes in the compartments by stochastic counting processes one can derive macroscopic models for large populations describing the average behavior by associated ordinary differential equations such as the celebrated SIR model. Further, diffusion approximations allow to address fluctuations from the average and to describe the state dynamics also for smaller populations by stochastic differential equations. In general, not all state variables are directly observable, and we face the so-called "dark figure" problem, which concerns, for example, the unknown number of asymptomatic and undetected infections. The present study addresses this problem by developing stochastic epidemic models that incorporate partial information about the current state of the epidemic, also known as nowcast uncertainty. Examples include a simple extension of the SIR model, a model for a disease with lifelong immunity after infection or vaccination, and a Covid-19 model. For the latter, we propose a ``cascade state approach'' that allows to exploit the information contained in formally hidden compartments with observable inflow but unobservable outflow. Furthermore, parameter estimation and calibration are performed using ridge regression for the Covid-19 model. The results of the numerical simulations illustrate the theoretical findings.
This paper presents a fundamental performance analysis of joint location and velocity estimation in a cell-free (CF) MIMO integrated sensing and communication (ISAC) system. Unlike prior studies that primarily rely on continuous-time signal models, we consider a more practical and challenging scenario in the discrete-time digital domain. Specifically, we first formulate a logarithmic likelihood function (LLF) and corresponding maximum likelihood estimation (MLE) for both single- and multiple-target sensing. Building upon the proposed LLF framework, closed-form Cramer-Rao lower bounds (CRLBs) for joint location and velocity estimation are derived under deterministic, unknown, and spatially varying radar cross-section (RCS) models. These CRLBs can serve as a fundamental performance metric to guide CF MIMO-ISAC system design. To enhance tractability, we also develop a class of simplified closed-form CRLBs, referred to as approximate CRLBs, along with a rigorous analysis of the conditions under which they remain accurate. Furthermore, we investigate how the sampling rate, squared effective bandwidth, and time width influence CRLB performance. For multi-target scenarios, the concepts of safety distance and safety velocity are introduced to characterize the conditions under which the CRLBs converge to their single-target counterparts. Extensive simulations using orthogonal frequency division multiplexing (OFDM) and orthogonal chirp division multiplexing (OCDM) validate the theoretical findings and provide practical insights for CF MIMO-ISAC system design
This article focuses on the development of functional unknown input observers for systems with arbitrary relative degree. Two distinct approaches are presented to address this challenge. The first approach is tailored to a class of time-varying systems expressed in a canonical controllable form. This method leverages the Generalized Parameter Estimation-Based Observer framework. The article derives the conditions for applicability of this solution and outlines the limitations on the number of estimable state variables. The second approach targets multi-input multi-output systems. In contrast to existing methods, the proposed solution is applicable to systems with arbitrary relative degree, significantly broadening its scope of application. The theoretical results are validated through simulation studies, which demonstrate the effectiveness of the proposed observers.
Cellular automata (CA) models are widely used to simulate complex systems with emergent behaviors, but identifying hidden parameters that govern their dynamics remains a significant challenge. This study explores the use of Convolutional Neural Networks (CNN) to identify jump parameters in a two-dimensional CA model. We propose a custom CNN architecture trained on CA-generated data to classify jump parameters, which dictates the neighborhood size and movement rules of cells within the CA. Experiments were conducted across varying domain sizes (25 x 25 to 150 x 150) and CA iterations (0 to 50), demonstrating that the accuracy improves with larger domain sizes, as they provide more spatial information for parameter estimation. Interestingly, while initial CA iterations enhance the performance, increasing the number of iterations beyond a certain threshold does not significantly improve accuracy, suggesting that only specific temporal information is relevant for parameter identification. The proposed CNN achieves competitive accuracy (89.31) compared to established architectures like LeNet-5 and AlexNet, while offering significantly faster inference times, making it suitable for real-time applications. This study highlights the potential of CNNs as a powerful tool for fast and accurate parameter estimation in CA models, paving the way for their use in more complex systems and higher-dimensional domains. Future work will explore the identification of multiple hidden parameters and extend the approach to three-dimensional CA models.
Mixture of experts (MoE) has recently emerged as an effective framework to advance the efficiency and scalability of machine learning models by softly dividing complex tasks among multiple specialized sub-models termed experts. Central to the success of MoE is an adaptive softmax gating mechanism which takes responsibility for determining the relevance of each expert to a given input and then dynamically assigning experts their respective weights. Despite its widespread use in practice, a comprehensive study on the effects of the softmax gating on the MoE has been lacking in the literature. To bridge this gap in this paper, we perform a convergence analysis of parameter estimation and expert estimation under the MoE equipped with the standard softmax gating or its variants, including a dense-to-sparse gating and a hierarchical softmax gating, respectively. Furthermore, our theories also provide useful insights into the design of sample-efficient expert structures. In particular, we demonstrate that it requires polynomially many data points to estimate experts satisfying our proposed \emph{strong identifiability} condition, namely a commonly used two-layer feed-forward network. In stark contrast, estimating linear experts, which violate the strong identifiability condition, necessitates exponentially many data points as a result of intrinsic parameter interactions expressed in the language of partial differential equations. All the theoretical results are substantiated with a rigorous guarantee.
The flexible loads in power systems, such as interruptible and transferable loads, are critical flexibility resources for mitigating power imbalances. Despite their potential, accurate modeling of these loads is a challenging work and has not received enough attention, limiting their integration into operational frameworks. To bridge this gap, this paper develops a data-driven identification theory and algorithm for price-responsive flexible loads (PRFLs). First, we introduce PRFL models that capture both static and dynamic decision mechanisms governing their response to electricity price variations. Second, We develop a data-driven identification framework that explicitly incorporates forecast and measurement errors. Particularly, we give a theoretical analysis to quantify the statistical impact of such noise on parameter estimation. Third, leveraging the bilevel structure of the identification problem, we propose a Bayesian optimization-based algorithm that features the scalability to large sample sizes and the ability to offer posterior differentiability certificates as byproducts. Numerical tests demonstrate the effectiveness and superiority of the proposed approach.
Large-scale battery energy storage systems (BESS) have found ever-increasing use across industry and society to accelerate clean energy transition and improve energy supply reliability and resilience. However, their optimal power management poses significant challenges: the underlying high-dimensional nonlinear nonconvex optimization lacks computational tractability in real-world implementation, and the uncertainty of the exogenous power demand makes exact optimization difficult. This paper presents a new solution framework to address these bottlenecks. The solution pivots on introducing power-sharing ratios to specify each cell's power quota from the output power demand. To find the optimal power-sharing ratios, we formulate a nonlinear model predictive control (NMPC) problem to achieve power-loss-minimizing BESS operation while complying with safety, cell balancing, and power supply-demand constraints. We then propose a parameterized control policy for the power-sharing ratios, which utilizes only three parameters, to reduce the computational demand in solving the NMPC problem. This policy parameterization allows us to translate the NMPC problem into a Bayesian inference problem for the sake of 1) computational tractability, and 2) overcoming the nonconvexity of the optimization problem. We leverage the ensemble Kalman inversion technique to solve the parameter estimation problem. Concurrently, a low-level control loop is developed to seamlessly integrate our proposed approach with the BESS to ensure practical implementation. This low-level controller receives the optimal power-sharing ratios, generates output power references for the cells, and maintains a balance between power supply and demand despite uncertainty in output power. We conduct extensive simulations and experiments on a 20-cell prototype to validate the proposed approach.
Parameter estimation in electrochemical models remains a significant challenge in their application. This study investigates the impact of different operating profiles on electrochemical model parameter estimation to identify the optimal conditions. In particular, the present study is focused on Nickel Manganese Cobalt Oxide(NMC) lithium-ion batteries. Based on five fundamental current profiles (C/5, C/2, 1C, Pulse, DST), 31 combinations of conditions were generated and used for parameter estimation and validation, resulting in 961 evaluation outcomes. The Particle Swarm Optimization is employed for parameter identification in electrochemical models, specifically using the Single Particle Model (SPM). The analysis considered three dimensions: model voltage output error, parameter estimation error, and time cost. Results show that using all five profiles (C/5, C/2, 1C, Pulse, DST) minimizes voltage output error, while {C/5, C/2, Pulse, DST} minimizes parameter estimation error. The shortest time cost is achieved with {1C}. When considering both model voltage output and parameter errors, {C/5, C/2, 1C, DST} is optimal. For minimizing model voltage output error and time cost, {C/2, 1C} is best, while {1C} is ideal for parameter error and time cost. The comprehensive optimal condition is {C/5, C/2, 1C, DST}. These findings provide guidance for selecting current conditions tailored to specific needs.
Hemodynamic parameters such as pressure and wall shear stress play an important role in diagnosis, prognosis, and treatment planning in cardiovascular diseases. These parameters can be accurately computed using computational fluid dynamics (CFD), but CFD is computationally intensive. Hence, deep learning methods have been adopted as a surrogate to rapidly estimate CFD outcomes. A drawback of such data-driven models is the need for time-consuming reference CFD simulations for training. In this work, we introduce an active learning framework to reduce the number of CFD simulations required for the training of surrogate models, lowering the barriers to their deployment in new applications. We propose three distinct querying strategies to determine for which unlabeled samples CFD simulations should be obtained. These querying strategies are based on geometrical variance, ensemble uncertainty, and adherence to the physics governing fluid dynamics. We benchmark these methods on velocity field estimation in synthetic coronary artery bifurcations and find that they allow for substantial reductions in annotation cost. Notably, we find that our strategies reduce the number of samples required by up to 50% and make the trained models more robust to difficult cases. Our results show that active learning is a feasible strategy to increase the potential of deep learning-based CFD surrogates.
In this paper, we consider near-field localization and sensing with an extremely large aperture array under partial blockage of array antennas, where spherical wavefront and spatial non-stationarity are accounted for. We propose an Ising model to characterize the clustered sparsity feature of the blockage pattern, develop an algorithm based on alternating optimization for joint channel parameter estimation and visibility region detection, and further estimate the locations of the user and environmental scatterers. The simulation results confirm the effectiveness of the proposed algorithm compared to conventional methods.
We consider the problem of joint input design and parameter estimation for identifying nonlinear system models through the sequential acquisition of measurements while adhering to system constraints. We utilize a receding horizon approach and propose a new scale-invariant input design criterion, which is tailored to continuously updated parameter estimates, along with a new sequential parameter estimator. We demonstrate the ability of the method to design informative experiments online, while steering the system within operational constraints.
Joint utilization of multiple discrete frequency bands can enhance the accuracy of delay estimation. Although some unique challenges of multiband fusion, such as phase distortion, oscillation phenomena, and high-dimensional search, have been partially addressed, further challenges remain. Specifically, under conditions of low signal-to-noise ratio (SNR), insufficient data, and closely spaced delay paths, accurately determining the model order-the number of delay paths-becomes difficult. Misestimating the model order can significantly degrade the estimation performance of traditional methods. To address joint model selection and parameter estimation under such harsh conditions, we propose a multi-model stochastic particle-based variational Bayesian inference (MM-SPVBI) framework, capable of exploring multiple high-dimensional parameter spaces. Initially, we split potential overlapping primary delay paths based on coarse estimates, generating several parallel candidate models. Then, an auto-focusing sampling strategy is employed to quickly identify the optimal model. Additionally, we introduce a hybrid posterior approximation to improve the original single-model SPVBI, ensuring overall complexity does not increase significantly with parallelism. Simulations demonstrate that our algorithm offers substantial advantages over existing methods.