Parameter Estimation

Motor unit parameters such as the innervation zone centre or the conduction velocity of the electrical potential harbour the potential to improve the fidelity of neuromechanical models used for movement and force prediction. Determining these parameters in a non-invasive way is challenging, as they are subject-specific and may vary with muscle contraction. Existing work on the estimation of motor unit parameters mainly relies on white-box modelling and therefore requires substantial manual modelling effort. This work targets the simultaneous estimation of multiple subject-specific motor unit parameters from electromyography (EMG) recordings measured non-invasively at the skin surface. This results in an inverse problem with a nonlinear loss function. To address this problem, an informed autoencoder is developed. This autoencoder reconstructs the surface EMG recordings while learning the parameters in its latent space and adhering to physical laws that relate the parameters to the EMG signals. In experiments on synthetic data, innervation zone centres are estimated with a mean absolute error of 2.5989 $\mathrm{mm}$, and conduction velocities of the electric potential are estimated with a mean absolute error of 0.1697 $\mathrm{m}\mathrm{s}^{-1}$. These results demonstrate the plausibility of this novel approach, which enables the simultaneous estimation of several motor unit parameters while reducing manual modelling effort through the integration of data-driven machine learning.

We study nonparametric estimation of Schrödinger bridge (SB) drifts from i.i.d.\ data observed on a single time interval. Starting from the conditional-ratio form of the Schrödinger bridge time-series (SBTS) drift formula, we analyze a direct Nadaraya--Watson plug-in estimator built from kernelized numerator and denominator terms. Unlike recent SB analyses based on entropic-OT potentials, Sinkhorn iterations, or iterative bridge solvers, our approach works directly at the drift level and isolates statistical error from optimization, approximation, and discretization error. Under Hölder regularity, a marginal-density floor, and bounded support, we prove a uniform non-asymptotic bound for admissible bandwidth pairs, a pointwise CLT under genuine undersmoothing, and an adaptive bandwidth selector satisfying an oracle inequality. We also prove a pivot-local minimax lower bound which, through an explicit uniform pivot, yields a global minimax lower bound under transparent compatibility conditions; hence the adaptive selector is minimax-rate optimal up to logarithmic factors. Synthetic experiments provide theorem-targeted diagnostics for finite-sample scaling, Gaussian approximation, and adaptive behavior.

Radar sounders are electromagnetic instruments that can probe deep into the subsurface of Earth and other planetary bodies by processing the echo of transmitted radar waves. Conventional approaches for analyzing such data rely on approximate assumptions and often produce point estimates that ignore parameter correlations as well as galactic and measurement noise. We propose a simulation-based inference approach to terrain parameter inversion from radar sounder data, where synthetic observations from a GPU-based simulator are used to train a neural network-based density estimator for neural posterior estimation (NPE). By explicitly conditioning on reference surface assumptions, the proposed framework allows systematic evaluation of posterior robustness to reference surface variability. We demonstrate that our NPE model is well calibrated on simulated data and transferable to real Mars radar profiles, where we analyze terrain parameters using literature-informed reference values.

Accurate, unified models for event cameras (ECs) remain elusive, hampering calibration and algorithm design. We develop a foundational probabilistic model for EC event detection, grounded in photon statistics, that unifies the description of static scene noise events and step response curves (S-curves) within a single analytical framework. Three formulations of the probability distributions are derived, spanning all intensity regimes: exact Poisson, saddle-point, and Gaussian. The model reveals the underlying connection between these otherwise disparate EC behaviors and clarifies the interpretation of S-curves, which we show is more nuanced than selecting a fixed probability threshold. Based on this model, we propose Noise2Params, a method for determining camera-specific values of the log-contrast threshold $B$, the lux-to-photon conversion factor $α$, and the leakage term $θ$ (found to be intensity dependent), via error minimization against observed noise-event distributions. Noise2Params requires only recordings of static, uniform scenes, offering an experimentally accessible alternative to approaches that demand specialized dynamic light sources. We further support the validity the model by training convolutional neural networks (CNNs) on synthetic noise images generated from our distributions and evaluating their ability to reconstruct static scenes from experimental data. We further demonstrate the utility of our model by showing that CNNs incorporating synthetic data outperform those trained solely on experimental data. Our framework provides a quantitative foundation for EC calibration, noise-aware algorithm design, and applications in photon-limited regimes.

This paper introduces an extension of generalised filtering for online applications. Generalised filtering refers to data assimilation schemes that jointly infer latent states, learn unknown model parameters, and estimate uncertainty in an integrated framework -- e.g., estimate state and observation noise -- at the same time (i.e., triple estimation). This framework appears across disciplines under different names, including variational Kalman-Bucy filtering in engineering, generalised predictive coding in neuroscience, and Dynamic Expectation Maximisation (DEM) in time-series analysis. Here, we specialise DEM for ``online'' data assimilation, through a separation of temporal scales. We describe the variational principles and procedures that allow one to assimilate data in a way that allows for a slow updating of parameters and precisions, which contextualise fast Bayesian belief updating about the dynamic hidden states. Using numerical studies, we demonstrate the validity of online DEM (ODEM) using a non-linear -- and potentially chaotic -- generative model, to show that the ODEM scheme can track the latent states of the generative process, even when its functional form differs fundamentally from the dynamics of the generative model. Framed from a neuro-mimetic predictive coding perspective, ODEM offers a biologically inspired solution to online inference, learning, and uncertainty estimation in dynamic environments.

Calibrating the urban underlying surface parameters is crucial for urban flood simulation. We formulate the parameter calibration problem into an optimization problem within the Bayesian framework using the maximum likelihood principle. We adopt the urban flood dynamical system model as the surrogate model and innovatively introduce latent variables inspired by machine learning to represent more uncertainties, which can also be compatible with common physical parameter calibration. For more efficient optimization, we construct the adjoint equation of the surrogate model to obtain gradient information and propose the parameter sharing technique and the localization technique to reduce the computation complexity of the adjoint equation. A simple case verifies the proposed method can converge quickly and is insensitive to the observation time interval. In the case derived from Test 8A, we calibrate Manning's coefficient of urban roads, with a maximum relative error of 13.88% and a minimum of 1.16%.

Learning-based approaches to verifying unknown Markov decision processes (MDPs) often employ uncertain MDPs. These models use, for example, confidence intervals to capture transition uncertainty and allow synthesis of policies that are robust to this uncertainty. However, this approach typically quantifies uncertainty independently for individual transition probabilities, ignoring dependencies due to shared latent quantities. We propose to learn such models using parametric MDPs (pMDPs), where transition probabilities are expressions over a set of parameters. We project statistical uncertainty from empirical transition frequencies onto the pMDP's parameter space, yielding a probably approximately correct (PAC) uncertainty model for the underlying MDP that respects the algebraic dependencies between transitions. The resulting models are algorithmically challenging to solve, so we propose a hierarchy of sound polytopic outer approximations of the induced confidence set. We implement and evaluate our approach, demonstrating substantially tighter uncertainty estimates than classical interval-based uncertain MDP learning techniques.

Closed-source frontier labs do not disclose parameter counts. Storing F facts requires at least F/(bits per parameter) weights, so factual recall lower-bounds parameter count--an intrinsic, serving-independent signal, though (as we show) a coarse one. We introduce Incompressible Knowledge Probes (IKPs), a benchmark of 1,400 factual questions spanning 7 tiers of obscurity, designed to isolate knowledge that cannot be derived by reasoning or compressed by architectural improvements. We score with no hallucination penalty (lambda = 0: IKP accuracy is simply the fraction of probed facts answered correctly), which removes both the penalty hyperparameter and the per-tier flooring choice; a full lambda x flooring ablation shows the calibration is robust across scoring choices while individual estimates are not, motivating the no-penalty default. We calibrate a log-linear mapping from IKP accuracy to parameter count on 93 open-weight models (135M-1,600B) spanning 19 vendors, achieving R^2 = 0.910; leave-one-out cross-validation confirms generalization (median fold error 1.48x, 72% within 2x, 86% within 3x). The instrument is deliberately coarse--its 90% prediction interval spans ~3x in either direction, wider than inference economics--so IKP recovers order-of-magnitude effective capacity and relative rankings, not precise parameter counts. For Mixture-of-Experts models, total parameters predict knowledge (R^2 = 0.67) better than active parameters (R^2 = 0.41). We evaluate 201 models from 27 vendors on a curated probe set (1,311 of 1,400 probes surviving name-collision and label-ambiguity filters) and report effective knowledge capacity for all major proprietary frontier models as prediction bands rather than point estimates; for heavily safety-tuned models these are lower bounds, since refusal policy can suppress tens of percentage points of otherwise-answerable capacity.

There has been remarkable progress over the past decade in establishing finite-sample, non-asymptotic bounds on recovering unknown system parameters from observed system behavior. Surprisingly, however, we show that the current state-of-the-art bounds do not accurately capture the statistical complexity of system identification, even in the most fundamental setting of estimating a discrete-time linear dynamical system (LDS) via ordinary least-squares regression (OLS). Specifically, we utilize asymptotic normality to identify classes of problem instances for which current bounds overstate the squared parameter error, in both spectral and Frobenius norm, by a factor of the state-dimension of the system. Informed by this discrepancy, we then sharpen the OLS parameter error bounds via a novel second-order decomposition of the parameter error, where crucially the lower-order term is a matrix-valued martingale that we show correctly captures the CLT scaling. From our analysis we obtain finite-sample bounds for both (i) stable systems and (ii) the many-trajectories setting that match the instance-specific optimal rates up to constant factors in Frobenius norm, and polylogarithmic state-dimension factors in spectral norm.

We study semisupervised mean estimation with a small labeled sample, a large unlabeled sample, and a black-box prediction model whose output may be miscalibrated. A standard approach in this setting is augmented inverse-probability weighting (AIPW) [Robins et al., 1994], which protects against prediction-model misspecification but can be inefficient when the prediction score is poorly aligned with the outcome scale. We introduce Calibrated Prediction-Powered Inference, which post-hoc calibrates the prediction score on the labeled sample before using it for semisupervised estimation. This simple step requires no retraining and can improve the original score both as a predictor of the outcome and as a regression adjustment for semisupervised inference. We study both linear and isotonic calibration. For isotonic calibration, we establish first-order optimality guarantees: isotonic post-processing can improve predictive accuracy and estimator efficiency relative to the original score and simpler post-processing rules, while no further post-processing of the fitted isotonic score yields additional first-order gains. For linear calibration, we show first-order equivalence to PPI++. We also clarify the relationship among existing estimators, showing that the original PPI estimator is a special case of AIPW and can be inefficient when the prediction model is accurate, while PPI++ is AIPW with empirical efficiency maximization [Rubin et al., 2008]. In simulations and real-data experiments, our calibrated estimators often outperform PPI and are competitive with, or outperform, AIPW and PPI++. We provide an accompanying Python package, ppi_aipw, at https://larsvanderlaan.github.io/ppi-aipw/.

In this work, we revisit the problem of active sequential prediction-powered mean estimation, where at each round one must decide the query probability of the ground-truth label upon observing the covariates of a sample. Furthermore, if the label is not queried, the prediction from a machine learning model is used instead. Prior work proposed an elegant scheme that determines the query probability by combining an uncertainty-based suggestion with a constant probability that encodes a soft constraint on the query probability. We explored different values of the mixing parameter and observed an intriguing empirical pattern: the smallest confidence width tends to occur when the weight on the constant probability is close to one, thereby reducing the influence of the uncertainty-based component. Motivated by this observation, we develop a non-asymptotic analysis of the estimator and establish a data-dependent bound on its confidence interval. Our analysis further suggests that when a no-regret learning approach is used to determine the query probability and control this bound, the query probability converges to the constraint of the max value of the query probability when it is chosen obliviously to the current covariates. We also conduct simulations that corroborate these theoretical findings.

Always-on converter health monitoring demands sub-mW edge inference, a regime inaccessible to GPU-based physics-informed neural networks. This work separates spiking temporal processing from physics enforcement: a three-layer leaky integrate-and-fire SNN estimates passive component parameters while a differentiable ODE solver provides physics-consistent training by decoupling the ODE physics loss from the unrolled spiking loop. On an EMI-corrupted synchronous buck converter benchmark, the SNN reduces lumped resistance error from $25.8\%$ to $10.2\%$ versus a feedforward baseline, within the $\pm 10\%$ manufacturing tolerance of passive components, at a projected ${\sim}270\times$ energy reduction on neuromorphic hardware. Persistent membrane states further enable degradation tracking and event-driven fault detection via a $+5.5$ percentage-point spike-rate jump at abrupt faults. With $93\%$ spike sparsity, the architecture is suited for always-on deployment on Intel Loihi 2 or BrainChip Akida.

Nonlinear system identification must balance physical interpretability with model flexibility. Classical methods yield structured, control-relevant models but rely on rigid parametric forms that often miss complex nonlinearities, whereas Neural ODEs are expressive yet largely black-box. Physics-Informed Neural Networks (PINNs) sit between these extremes, but inverse PINNs typically assume a known governing equation with fixed coefficients, leading to identifiability failures when the true dynamics are unknown or state-dependent. We propose SOLIS, which models unknown dynamics via a state-conditioned second-order surrogate model and recasts identification as learning a Quasi-Linear Parameter-Varying (Quasi-LPV) representation, recovering interpretable natural frequency, damping, and gain without presupposing a global equation. SOLIS decouples trajectory reconstruction from parameter estimation and stabilizes training with a cyclic curriculum and Local Physics Hints windowed ridge-regression anchors that mitigate optimization collapse. Experiments on benchmarks show accurate parameter-manifold recovery and coherent physical rollouts from sparse data, including regimes where standard inverse methods fail.

Weak gravitational lensing, the correlated distortion of background galaxy shapes by foreground structures, is a powerful probe of the matter distribution in our universe and allows accurate constraints on the cosmological model. In recent years, high-order statistics and machine learning (ML) techniques have been applied to weak lensing data to extract the nonlinear information beyond traditional two-point analysis. However, these methods typically rely on cosmological simulations, which poses several challenges: simulations are computationally expensive, limiting most realistic setups to a low training data regime; inaccurate modeling of systematics in the simulations create distribution shifts that can bias cosmological parameter constraints; and varying simulation setups across studies make method comparison difficult. To address these difficulties, we present the first weak lensing benchmark dataset with several realistic systematics and launch the FAIR Universe Weak Lensing Machine Learning Uncertainty Challenge. The challenge focuses on measuring the fundamental properties of the universe from weak lensing data with limited training set and potential distribution shifts, while providing a standardized benchmark for rigorous comparison across methods. Organized in two phases, the challenge will bring together the physics and ML communities to advance the methodologies for handling systematic uncertainties, data efficiency, and distribution shifts in weak lensing analysis with ML, ultimately facilitating the deployment of ML approaches into upcoming weak lensing survey analysis.

The exponential growth of data from modern radio telescopes presents a significant challenge to traditional single-pulse search algorithms, which are computationally intensive and prone to high false-positive rates due to Radio Frequency Interference (RFI). In this work, we introduce FRTSearch, an end-to-end framework unifying the detection and physical characterization of Fast Radio Transients (FRTs). Leveraging the morphological universality of dispersive trajectories in time-frequency dynamic spectra, we reframe FRT detection as a pattern recognition problem governed by the cold plasma dispersion relation. To facilitate this, we constructed CRAFTS-FRT, a pixel-level annotated dataset derived from the Commensal Radio Astronomy FAST Survey (CRAFTS), comprising 2{,}392 instances across diverse source classes. This dataset enables the training of a Mask R-CNN model for precise trajectory segmentation. Coupled with our physics-driven IMPIC algorithm, the framework maps the geometric coordinates of segmented trajectories to directly infer the Dispersion Measure (DM) and Time of Arrival (ToA). Benchmarking on the FAST-FREX dataset shows that FRTSearch achieves a 98.0% recall, competitive with exhaustive search methods, while reducing false positives by over 99.9% compared to PRESTO and delivering a processing speedup of up to $13.9\times$. Furthermore, the framework demonstrates robust cross-facility generalization, detecting all 19 tested FRBs from the ASKAP survey without retraining. By shifting the paradigm from search-then-identify'' to detect-and-infer,'' FRTSearch provides a scalable, high-precision solution for real-time discovery in the era of petabyte-scale radio astronomy.

Global ocean models exhibit biases in the mean state and variability, particularly at coarse resolution, where mesoscale eddies are unresolved. To address these biases, parameterization coefficients are typically tuned ad hoc. Here, we formulate parameter tuning as a calibration problem using Ensemble Kalman Inversion (EKI). We optimize parameters of a neural network parameterization of mesoscale eddies in two idealized ocean models at coarse resolution. The calibrated parameterization reduces errors by factors of 1.7-3.3 in the time-averaged fluid interfaces and their variability compared to the unparameterized model, depending on the metric and configuration. The EKI method is robust to noise in time-averaged statistics arising from chaotic ocean dynamics. Furthermore, we propose an efficient calibration protocol that bypasses integration to statistical equilibrium by carefully choosing an initial condition. These results demonstrate that systematic calibration can substantially improve coarse-resolution ocean simulations and provide a practical pathway for reducing biases in global ocean models.

Gray-box RC models are widely used to enable energy-efficient model predictive control (MPC) in buildings. However, estimating RC parameters remains difficult, as conventional optimization-based algorithms are prone to local minima, rely heavily on good initial guesses, and incur high computational cost. To address these issues, we propose the Estimator from Scratch, a novel neural parameter estimation approach that embeds the physical equations into a neural network's training process to estimate RC parameters. To further improve estimation accuracy and eliminate dependence on an initial guess, we extend this approach by pretraining the neural network on data from multiple source buildings, the Pretrained Estimator. We benchmark both methods against a genetic-algorithm-based RC estimator and a fully black-box neural network. All methods are evaluated across eight simulated and three real-world buildings for two RC configurations, for both prediction accuracy and closed-loop MPC performance, the latter only for the simulated buildings. The Pretrained Estimator achieves the best prediction performance among all RC-based methods, particularly with little training data, and yields the lowest and least variable MPC costs across buildings and benchmarks. These results position the Pretrained Estimator as a robust, computationally efficient, and initial-guess-free alternative for RC parameter estimation, with potential to extend to other control-oriented dynamical systems.

Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood flow model that describes the viscoelastic properties of arterial walls, and we focus on improving its practical applicability by addressing a major challenge: determining, in a reliable way, the viscoelastic parameters that control how arteries deform under pulsatile pressure. To achieve this, we employ Asymptotic-Preserving Neural Networks that embed the governing physical principles of the multiscale viscoelastic blood flow model within the learning procedure. This framework allows us to infer the viscoelastic parameters while simultaneously reconstructing the time-dependent evolution of the state variables of blood vessels. With this approach, pressure waveforms are estimated from readily accessible patient-specific data, i.e., cross-sectional area and velocity measurements from Doppler ultrasound, in vascular segments where direct pressure measurements are not available. Different numerical simulations, conducted in both synthetic and patient-specific scenarios, show the effectiveness of the proposed methodology.

Damped sinusoidal oscillations are widely observed in many physical systems, and their analysis provides access to underlying physical properties. However, parameter estimation becomes difficult when the signal decays rapidly, multiple components are superposed, and observational noise is present. In this study, we develop an autoencoder-based method that uses the latent space to estimate the frequency, phase, decay time, and amplitude of each component in noisy multi-component damped sinusoidal signals. We investigate multi-component cases under Gaussian-distribution training and further examine the effect of the training-data distribution through comparisons between Gaussian and uniform training. The performance is evaluated through waveform reconstruction and parameter-estimation accuracy. We find that the proposed method can estimate the parameters with high accuracy even in challenging setups, such as those involving a subdominant component or nearly opposite-phase components, while remaining reasonably robust when the training distribution is less informative. This demonstrates its potential as a tool for analyzing short-duration, noisy signals.

Stochastic kinetic models are ubiquitous in physics, yet inferring their parameters from experimental data remains challenging. For deterministic models, parameter inference often relies on gradients, which can be obtained efficiently through automatic differentiation (AD). However, AD cannot be applied directly to the Gillespie stochastic simulation algorithm (SSA), since sampling from a discrete set of reactions introduces non-differentiable operations. In this work, we adopt three gradient estimators from machine learning for the Gillespie SSA: the Gumbel-Softmax Straight-Through (GS-ST) estimator, the Score Function estimator, and the Alternative Path estimator. We use the estimators to evaluate gradients of steady-state and time-dependent observables, and compare their performance in representative biophysical systems with relaxation dynamics (bimolecular association) and oscillatory dynamics (repressilator). We find that the GS-ST estimator generally yields well-behaved gradient estimates, but exhibits diverging variance in challenging parameter regimes, which can cause parameter inference to fail. In these cases, other estimators provide more robust, lower variance gradients. Our results demonstrate that gradient-based parameter inference can be effectively combined with the Gillespie SSA, with different estimators offering complementary advantages.

Deep learning has shown strong potential for scientific discovery, but its ability to model macroscopic rigid-body kinematic constraints remains underexplored. We study this problem on spatial over-constrained mechanisms and propose O-ConNet, an end-to-end framework that infers mechanism structural parameters from only three sparse reachable points while reconstructing the full motion trajectory, without explicitly solving constraint equations during inference. On a self-constructed Bennett 4R dataset of 42,860 valid samples, O-ConNet achieves Param-MAE 0.276 +/- 0.077 and Traj-MAE 0.145 +/- 0.018 (mean +/- std over 10 runs), outperforming the strongest sequence baseline (LSTM-Seq2Seq) by 65.1 percent and 88.2 percent, respectively. These results suggest that end-to-end learning can capture closed-loop geometric structure and provide a practical route for inverse design of spatial over-constrained mechanisms under extremely sparse observations.

We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function approximation. SKINNs jointly estimate neural network parameters and economically meaningful structural parameters in a single optimization problem, enforcing theoretical consistency not only on observed data but over a broader input domain through collocation, and therefore nesting approaches such as functional GMM, Bayesian updating, transfer learning, PINNs, and surrogate modeling. SKINNs define a class of M-estimators that are consistent and asymptotically normal with root-N convergence, sandwich covariance, and recovery of pseudo-true parameters under misspecification. We establish identification of structural parameters under joint flexibility, derive generalization and target-risk bounds under distributional shift in a convex proxy, and provide a restricted-optimal characterization of the weighting parameter that governs the bias-variance tradeoff. In an illustrative financial application to option pricing, SKINNs improve out-of-sample valuation and hedging performance, particularly at longer horizons and during high-volatility regimes, while recovering economically interpretable structural parameters with improved stability relative to conventional calibration. More broadly, SKINNs provide a general econometric framework for combining model-based reasoning with high-dimensional, data-driven estimation.

Diffusion MRI microstructure fitting is nonconvex and often performed voxelwise, which limits fiber peak recovery in narrow crossings. This work introduces PRISM, a differentiable analysis-by-synthesis framework that fits an explicit multi-compartment forward model end-to-end over spatial patches. The model combines cerebrospinal fluid (CSF), gray matter, up to K white-matter fiber compartments (stick-and-zeppelin), and a restricted compartment, with explicit fiber directions and soft model selection via repulsion and sparsity priors. PRISM supports a fast MSE objective and a Rician negative log-likelihood (NLL) that jointly learns sigma without oracle information. A lightweight nuisance calibration module (smooth bias field and per-measurement scale/offset) is included for robustness and regularized to identity in clean-data tests. On synthetic crossing-fiber data (SNR=30; five methods, 16 crossing angles), PRISM achieves 3.5 degrees best-match angular error with 95% recall, which is 1.9x lower than the best baseline (MSMT-CSD, 6.8 degrees, 83% recall); in NLL mode with learned sigma, error drops to 2.3 degrees with 99% recall, resolving crossings down to 20 degrees. On the DiSCo1 phantom (NLL mode), PRISM improves connectivity correlation over CSD baselines at all four tracking angles (best r=.934 at 25 degrees vs. .920 for MSMT-CSD). Whole-brain HCP fitting (~741k voxels, MSE mode) completes in ~12 min on a single GPU with near-identical results across random seeds.

This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we leverage the Wiener Chaos Expansion (WCE), a spectral decomposition technique that projects the stochastic solution onto an orthogonal basis of Hermite polynomials. This transformation effectively maps the stochastic dynamics into a hierarchical system of deterministic functions, termed the propagator. By reducing the stochastic inference task to a deterministic optimization problem, our framework circumvents the heavy computational burden and sampling requirements of traditional simulation-based methods like MCMC or MLE. The robustness and scalability of the proposed approach are demonstrated through numerical experiments on various non-linear SDEs, including models for individual biological growth. Results show that the WCE-SGD framework provides accurate parameter recovery even from discrete, noisy observations, offering a significant paradigm shift in the efficient modeling of complex stochastic systems.

This paper presents an online path planning algorithm for safe autonomous manipulation of a flexibly constrained object in an unknown environment. Methods for real time identification and characterization of perceived flexible constraints and global stiffness are presented. Used in tandem, these methods allow a robot to simultaneously explore, characterize, and manipulate an elastic system safely. Navigation without a-priori knowledge of the system is achieved using constraint exploration based on local force and position information. The perceived constraint stiffness is considered at multiple poses along an object's (system) trajectory. Using stiffness eigenvector information, global stiffness behavior is characterized and identified using an atlas of simple mechanical constraints, such as hinges and planar constraints. Validation of these algorithms is carried out by simulation and experimentally. The ability to recognize several common simple mechanical constraints (such as a flexible hinge) in real time, and to subsequently identify relevant screw parameters is demonstrated. These results suggest the feasibility of simultaneous global constrain/stiffness exploration and safe manipulation of flexibly constrained objects. We believe that this approach will eventually enable safe cooperative manipulation in applications such as organ retraction and manipulation during surgery

The Event Horizon Telescope (EHT) delivered the first image of a black hole by capturing the light from its surrounding accretion flow, revealing structure but not dynamics. Simulations of black hole accretion dynamics are essential for interpreting EHT images but costly to generate and impractical for inference. Motivated by this bottleneck, BHCast presents a framework for forecasting black hole plasma dynamics from a single, blurry snapshot, such as those captured by the EHT. At its core, BHCast is a neural model that transforms a static image into forecasted future frames, revealing the underlying dynamics hidden within one snapshot. With a multi-scale pyramid loss, we demonstrate how autoregressive forecasting can simultaneously super-resolve and evolve a blurry frame into a coherent, high-resolution movie that remains stable over long time horizons. From forecasted dynamics, we can then extract interpretable spatio-temporal features, such as pattern speed (rotation rate) and pitch angle. Finally, BHCast uses gradient-boosting trees to recover black hole properties from these plasma features, including the spin and viewing inclination angle. The separation between forecasting and inference provides modular flexibility, interpretability, and robust uncertainty quantification. We demonstrate the effectiveness of BHCast on simulations of two distinct black hole accretion systems, Sagittarius A* and M87*, by testing on simulated frames blurred to EHT resolution and real EHT images of M87*. Ultimately, our methodology establishes a scalable paradigm for solving inverse problems, demonstrating the potential of learned dynamics to unlock insights from resolution-limited scientific data.

The increasing demand for augmented reality and robotics is driving the need for articulated object reconstruction with high scalability. However, existing settings for reconstructing from discrete articulation states or casual monocular videos require non-trivial axis alignment or suffer from insufficient coverage, limiting their applicability. In this paper, we introduce FreeArtGS, a novel method for reconstructing articulated objects under free-moving scenario, a new setting with a simple setup and high scalability. FreeArtGS combines free-moving part segmentation with joint estimation and end-to-end optimization, taking only a monocular RGB-D video as input. By optimizing with the priors from off-the-shelf point-tracking and feature models, the free-moving part segmentation module identifies rigid parts from relative motion under unconstrained capture. The joint estimation module calibrates the unified object-to-camera poses and recovers joint type and axis robustly from part segmentation. Finally, 3DGS-based end-to-end optimization is implemented to jointly reconstruct visual textures, geometry, and joint angles of the articulated object. We conduct experiments on two benchmarks and real-world free-moving articulated objects. Experimental results demonstrate that FreeArtGS consistently excels in reconstructing free-moving articulated objects and remains highly competitive in previous reconstruction settings, proving itself a practical and effective solution for realistic asset generation. The project page is available at: https://freeartgs.github.io/

Neutrino oscillations encode fundamental information about neutrino masses and mixing parameters, offering a unique window into physics beyond the Standard Model. Estimating these parameters from oscillation probability maps is, however, computationally challenging due to the maps' high dimensionality and nonlinear dependence on the underlying physics. Traditional inference methods, such as likelihood-based or Monte Carlo sampling approaches, require extensive simulations to explore the parameter space, creating major bottlenecks for large-scale analyses. In this work, we introduce a data-driven framework that reformulates atmospheric neutrino oscillation parameter inference as a supervised regression task over structured oscillation maps. We propose a hierarchical transformer architecture that explicitly models the two-dimensional structure of these maps, capturing angular dependencies at fixed energies and global correlations across the energy spectrum. To improve physical consistency, the model is trained using a surrogate simulation constraint that enforces agreement between the predicted parameters and the reconstructed oscillation patterns. Furthermore, we introduce a neural network-based uncertainty quantification mechanism that produces distribution-free prediction intervals with formal coverage guarantees. Experiments on simulated oscillation maps under Earth-matter conditions demonstrate that the proposed method is comparable to a Markov Chain Monte Carlo baseline in estimation accuracy, with substantial improvements in computational cost (around 240$\times$ fewer FLOPs and 33$\times$ faster in average processing time). Moreover, the conformally calibrated prediction intervals remain narrow while achieving the target nominal coverage of 90%, confirming both the reliability and efficiency of our approach.

This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Our analysis considers trajectory-dependent regressors and allows marginally stable dynamics with polynomial mean-square state growth. We prove that the diameter of the feasible parameter set shrinks with sample complexity $\widetilde{\mathcal O}(1/ε)$ where $ε$ is the estimation error. Simulation supports the theory and illustrates the advantage of the proposed estimator for uncertainty quantification.

Estimating covariance matrices is fundamental to a wide range of statistical applications. This paper studies minimax and adaptive estimation of high-dimensional covariance matrices under $ρ$-zero-concentrated differential privacy ($ρ$-zCDP) over three nested classes: the pointwise-decay class $\mathcal{H}_α$, the row-tail class $\mathcal{G}_α$, and the separated-block class $\mathcal{F}_α$. We consider both squared operator norm loss and normalized squared Frobenius norm loss. For $\mathcal{H}_α$ and $\mathcal{G}_α$, we develop center--outer dyadic estimators tailored to the refined geometry of the two classes, while for $\mathcal{F}_α$, we develop a blockwise tridiagonal estimator. The resulting minimax-optimal rates reveal a nontrivial interplay among the smoothness $α$, the loss, the geometry of the covariance class, and the privacy constraint. In contrast to the non-private setting, privacy distinguishes covariance classes that share the same leading non-private rate and induces a polynomial dependence on the ambient dimension. We further develop procedures that adapt to the unknown decay parameter over all three covariance classes under both losses, at the cost of at most polylogarithmic factors. To establish minimax lower bounds, we develop a novel differentially private van Trees inequality that connects Fisher information with the $ρ$-zCDP constraint and may be useful for other private estimation problems. We also construct carefully designed prior distributions to obtain matching minimax lower bounds.