Parameter Estimation

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9 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 84

Oct 6, 2026physics.chem-ph

Learning consistent molecular mechanics force fields from first principles

Classical force fields (FFs) remain the workhorse for large-scale simulations even as machine-learned interatomic potentials (MLIPs) approach ab initio accuracy. They decompose total configuration energies into simple effective interactions whose parameters are traditionally assigned based on atom or bond types, enabling efficient simulations but also limiting their ability to adapt across configurations. Recent machine learning approaches have improved the accuracy and transferability of bonded parameters in these FFs by inferring them as functions of local atomic environments, but still rely on empirical nonbonded parameters for practical simulations. In this work, we introduce a unified approach, \texttt{grappa-fullFF}, which learns both bonded and nonbonded parameters \emph{consistently} and simultaneously from ab initio reference data. By incorporating physically inspired regularization via supervision of the electrostatic potential and an architecture that facilitates charge equilibration, our model recovers accurate electric response properties, achieves state-of-the-art accuracy on geometry optimization benchmarks, and reproduces the conformational sampling of both classical and existing machine-learned FFs, without relying on externally assigned nonbonded parameters.

Berkay Günes, Leif Seute, Jigyasa Nigam +1

Max Planck Institute for Polymer Research Mainz, Germany · Heidelberg University, Germany · Heidelberg Institute for Theoretical Studies, Germany +1

Parameter Estimation Molecular Dynamics Simulation

Oct 5, 2026cs.LG

Parameter Estimation in Machining Dynamics with Regenerative Delay and Nonsmooth Friction using Physics-Informed Neural Networks

A multi-domain eXtended Physics-Informed Neural Network (XPINN) framework is developed for nonsmooth Delay Differential Equations (DDEs). This is the first implementation to demonstrate the efficacy of partitioning the temporal domain into subdomains of integer multiples of the characteristic time delay and progressively training the associated subnetworks while freezing previously learned parameters. The efficacy of the proposed framework is demonstrated using a machining dynamics model that incorporates both regenerative and nonsmooth frictional effects. Results demonstrate that the proposed multi-domain XPINN framework leads to better solution reconstruction in DDEs and improved parameter estimation compared to a generic PINN (SPINN) formulation. The proposed method works particularly well for extended temporal domains and non-constant history functions. The robustness of inverse XPINN (I-XPINN) is also assessed using reference data contaminated with Gaussian measurement noise. Results indicate that I-XPINN remains resilient to measurement noise and the physics-informed constraints guide the network toward accurately recovering the underlying dynamics. This demonstrates, for the first time, the potential of the proposed framework for reliable parameter identification in DDEs characterised by nonsmoothness and large time delays.

Meiyazhagan Jaganathan, Vikram Pakrashi, Aasifa Rounak

UCD Centre for Mechanics, Dynamical Systems and Risk Laboratory, School of Mechanical and Materials Engineering, University College Dublin, D04 V1W8, Dublin, Ireland

Dynamical Systems Parameter Estimation Physics-Informed ML

Oct 5, 2026stat.ML

Learning Decision-Stump Thresholds in Context: Dynamics of Softmax Attention

Estimating a decision threshold requires locating observations near an unknown boundary. We study how gradient-based pretraining learns this statistical rule in a two-parameter softmax-attention model with a fixed feature and inequality direction. Pretraining uses labeled contexts and their true thresholds; a fresh threshold must be inferred from context alone. Under a large-resolution initialization, constant-step gradient descent on

m

tasks with

n

examples each produces a frozen estimator with error

\widetilde O((m\wedge n)^{-1}+N^{-1})

for each fixed interior threshold and every fresh-context size

N

. The two terms separate finite-pretraining accuracy from fresh-context localization. The mechanism is coordinated parameter divergence: population training calibrates the relative label and feature scores, then increases the attention scale as

t^{1/4}

, giving population threshold error

O(t^{-1/4})

. To transfer this mechanism to a fixed finite corpus, we control gradient errors relative to the shrinking directions of progress at successive parameter scales. This certifies a growing training interval without requiring long-time tracking of the population trajectory. We also identify the boundary limitation of the one-head model and explain statistically what a reflected symmetrization could achieve.

Hong Ha Le, Jackie Lok, Atsushi Nitanda +1

National University of Singapore · Princeton University · Nanyang Technological University

Language Model Pretraining Softmax Attention Parameter Estimation Gradient Descent In-Context Learning

Sep 30, 2026stat.ML

Inference for stochastic differential equations driven by weighted sub-fractional Brownian motion using neural networks and the Euler approximation

We consider the estimation of drift, diffusion, and noise covariance from discrete observations of stochastic differential equations driven by Gaussian processes. For a fixed observation horizon

T>0

and a known initial state

x_0\in\mathbb R

, we study \begin{equation*} dX_t=a(X_t),dt+σ(X_t),dZ_t^{β,f}, \qquad X_0=x_0,\quad 0\leq t\leq T. \end{equation*} \smallskip\noindent Here

a:\mathbb R\to\mathbb R

is the drift coefficient,

σ:\mathbb R\to(0,\infty)

is the diffusion coefficient, and

Z^{β,f}

is a centered Gaussian process from the weighted sub-fractional Brownian family, with covariance \begin{equation*} \operatorname{Cov}(Z_s^{β,f},Z_t^{β,f}) =\int_0^{s\wedge t} f(r)q_β(s-r,t-r),dr, \qquad 0\leq s,t\leq T. \end{equation*} \smallskip\noindent Here

s\wedge t=\min\{s,t\}

. The temporal weight

f:[0,T]\to[0,\infty)

is measurable, bounded, and positive almost everywhere, and

β\in(0,2)

is the covariance exponent. For

u,v\geq0

, the kernel is

q_β(u,v)=[u^β+v^β-(u+v)^β]/(1-β)

when

β\ne1

. Its continuous extension at

β=1

is

q_1(u,v)=(u+v)\log(u+v)-u\log u-v\log v

, with

0\log0=0

. Using the Euler approximation, we reconstruct the Gaussian driving increments from observed transitions and use their joint density to obtain a trajectory likelihood. Neural and radial-basis representations model the drift, diffusion, and normalized temporal weight, while a likelihood profile estimates the covariance exponent and diffusion scale. We compare the method with two neural alternatives on the same simulated trajectories in twenty coefficient settings.

J. H. Ramirez-Gonzalez

Institute of Mathematics and Statistics, University of São Paulo (IME–USP), São Paulo, Brazil

Parameter Estimation Stochastic Differential Equations Covariance Estimation

Sep 30, 2026cs.LG

On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability

Physical parameter estimation from video aims to recover the parameters of a known family of governing dynamical equations from pixel observations. Existing identifiability theory for this setting has focused on linear time-invariant (LTI) second-order systems, leaving open what can be identified for nonlinear scalar dynamics. We develop an identifiability theory for nonlinear scalar second-order ODEs, organized by how their velocity dependence interacts with changes of the learned state coordinate. Under a shared non-collapsed state map and explicit same-state velocity-coverage conditions, we show that parameter identifiability depends on the ODE family: some parameters are uniquely identifiable, while in other families only invariant parameter combinations are identifiable or external physical calibration is required. For laws that are at most linear in velocity, compatibility forces affine coordinate alignment, yielding explicit parameter relations, invariants, and calibration conditions. This affine conclusion extends to broader finite velocity-feature families when coordinate curvature can be separated from the declared velocity dependence. For families admitting a squared-velocity term, nonlinear coordinate ambiguity can remain; a law-derived normalization instead enables affine comparison between canonical laws. Experiments on synthetic systems and real pendulum and free-fall videos support the predicted parameter relations, coverage effects, and calibration requirements.

Wenjie Wang, Yuanyuan Wang, Zixiang Jiang +2

University of Melbourne · Mohamed bin Zayed University of Artificial Intelligence · Carnegie Mellon University

Parameter Estimation Parameter Identifiability Nonlinear System Identification Physical Reasoning in Video

Sep 29, 2026math.NA

Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest

This paper introduces a hybrid joint-selective optimization (HJSO) framework for large-scale numerical problems in which a small subset of trainable quantities is of primary interest. We partition the full parameter vector into a high-dimensional remaining block and a low-dimensional block of parameters of interest (POIs), perform joint first-order optimization over the full parameter set, and then freeze the remaining variables while applying a reduced-space Levenberg-Marquardt (LM) refinement to the POIs. The method is designed for settings in which the POIs are low-dimensional but strongly influence the quality of the computed solution, while the full parameter space remains too large for full-space second-order methods. The framework is evaluated on three representative problems: a matrix eigenvalue problem, an inverse Bratu problem solved with a physics-informed neural network, and a 100-dimensional nonlinear Black-Scholes problem solved with the DeepBSDE method. In each test, HJSO reaches prescribed POI-error thresholds faster than the corresponding joint first-order baseline and improves the final POI accuracy for the reported solver configurations. The contribution is therefore not a universal optimizer, but a practical reduced-space strategy for problems with known low-dimensional parameters of interest and expensive high-dimensional training variables.

Muhammad Luthfi Shahab, Gabriella Alfa Indahsari, Imam Mukhlash +1

Department of Mathematics, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia · Department of Mathematics, Khalifa University of Science & Technology, Abu Dhabi, PO Box 127788, United Arab Emirates

Parameter Estimation Second-Order Optimization

Sep 28, 2026eess.AS

Simulation-Based Inference for Plate Reverb System Identification

We address Task A of the 1st DAFx Parameter Estimation Challenge, which aims to retrieve the physical parameters of a plate model from an impulse response. To do so, we use the Simulation-Based Inference (SBI) framework, in which we train a neural network to estimate a density over plate parameters given an impulse response, using a dataset generated by the simulator. Inference for a new impulse response then requires only a forward pass through the network, without involving the simulator. For each test observation, we fine-tune a specific network: additional simulation rounds are performed by sampling parameters from the current estimated distribution, simulating the corresponding impulse responses, and fine-tuning to produce the specialized network.

Dylan Sechet, Marc Evrard, Matthieu Kowalski

Laboratoire Interdisciplinaire des Sciences du Numérique Université Paris-Saclay, Inria, CNRS, CentraleSupélec

Parameter Estimation Bayesian Inverse Problems

Sep 28, 2026q-bio.QM

Uncertainty Quantification in Cardiac Model Personalisation from Ultrafast Ultrasound

Cardiac model personalisation requires inferring mechanical parameters that are not directly measurable in vivo. Ultrafast ultrasound shear wave elastography (SWE) enables non-invasive tracking of myocardial stiffness dynamics over the cardiac cycle, providing a target for personalisation. However, mapping these observations to subject specific model parameters remains ill-posed, as multiple parameter sets can reproduce the same stiffness dynamics. We formulate SWE-informed personalisation as a statistical inference problem using simulation-based inference (SBI). Using a subject-adapted 0D cardiovascular model and neural posterior estimation, we estimate model-conditional posterior distributions over active stiffness scale k0, contraction rate kATP, and relaxation rate kSR, conditioned on SWE-derived curve features and subject specific context. Among six healthy volunteers, four passed objective prior-support diagnostics and were retained for quantitative posterior analysis. Curve-level RMSE against the observed SWE target decreased from 12.61

\pm

5.55 kPa for the prior predictive median to 1.14

\pm

0.38 kPa for the posterior predictive median, an 89.7

\pm

4.2% reduction. Posterior analysis revealed parameter-specific uncertainty, k0-kATP compensation, weaker constraint of kSR, and the importance of prior-predictive diagnostics for assessing whether each subject is represented within the modelled SWE feature space. These results support SBI for uncertainty aware SWE-based personalisation, while identifying prior support and forward-model adequacy as key diagnostics.

Camilla Ferrario, Maelys Venet, Olivier Villemain +1

CHU Bordeaux · EPIONE

Parameter Estimation Uncertainty Quantification

Sep 22, 2026stat.ML

Error Bounds for Statistical Estimators in BTL Model with Parametric Multivariate Utility Functions

We study preference elicitation under the Bradley-Terry-Luce (BTL) model where the true partworth vector is unknown and has to be estimated as a parameter with elicited preference information. The set of selected pairwise queries is non-uniform, deterministic, and arbitrary over a collection of alternatives, provided that it satisfies a joint identifiability condition. We focus on understanding when the canonical maximum likelihood estimator (MLE) is finite and admits sharp error bounds without explicit compactness constraints on the feasible set or external regularizers. To this end, we derive minimax lower bounds under the standard bounded dynamic range condition, and find that the same Fisher-information geometry in the classic Cramér-Rao lower bounds underpins the finite-sample difficulty of the estimation problem. By combining a non-asymptotic expansion of the likelihood score equation with a fixed-point localization argument, we identify a design-dependent sample size threshold above which the unconstrained canonical MLE exists and is unique with high probability. The same expansion yields a decomposition of the estimation error into a linear stochastic term, an explicit second-order bias, and a higher-order remainder. A refined analysis gives sufficient sample size conditions under which the canonical MLE attains the minimax rates up to logarithmic and constant factors. These results provide a unified non-asymptotic theory for parametric utility elicitation and reveal when the inference is determined by response data alone rather than by external regularization. Preliminary numerical results are consistent with the theoretical findings.

Yicheng Li, Huifu Xu

Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong.

Parameter Estimation Minimax Estimation Bradley–Terry Model Preference Elicitation

Sep 22, 2026stat.ML

Statistical Gains from Looped Estimation under Parameter Budgets

Memory constraints in artificial intelligence motivate accurate function approximation with fewer parameters. We study looping, which repeatedly composes one update function with shared parameters; each output becomes the next input. A looped Transformer, for example, reuses one block, whereas its conventional untied counterpart uses separately parameterized blocks. We compare their parameter requirements for a given worst-case approximation accuracy, or equivalently, their approximation accuracy under a common budget limiting distinct trainable coefficients. We then ask whether this representational parsimony improves statistical accuracy. For general likelihood models, we establish an upper squared Hellinger risk bound for looped sieve maximum likelihood and a minimax lower bound for the jointly tuned untied family. Further loop iterations improve the approximation bound without adding parameters, while increasing computation and the fitted-class complexity bound. For targets of known Hölder smoothness, looped residual feedforward networks and post-layer-normalized Transformers attain the minimax polynomial rate up to logarithmic factors with a fixed number of bounded real parameters. At sufficiently large fixed budgets, looped worst-case risk vanishes while optimal worst-case untied risk remains bounded away from zero. The loop-to-untied risk ratio also tends to zero under specified growing-budget conditions. Regression, binary response, and energy-based generative models illustrate the theory.

Xinyu Tian, Xiaotong Shen

School of Statistics, University of Minnesota

Parameter Estimation Minimax Estimation Neural Network Approximation Theory Statistical Learning Theory

Sep 17, 2026cs.LG

One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady State

We study the problem of recovering the parameters of a multivariate Ornstein-Uhlenbeck (OU) process from steady-state observational and interventional data. In many applications, such as large-scale gene perturbation experiments, only stationary "snapshot" measurements are available, making standard stochastic differential equation estimation methods that rely on time-series trajectories inapplicable. We first establish an identifiability result: one intervention per strongly connected component (SCC) of the drift graph suffices to recover all OU process parameters generically up to a global scaling factor. This holds provided that the SCC condensation graph is connected with a single root and certain spectral nondegeneracy assumptions hold. We propose a recursive learning algorithm that orders SCCs topologically and, for each component, isolates its marginal dynamics and solves a linear system derived from the steady-state moment equations, leveraging parameters recovered for upstream components. Building on this theoretical foundation, we propose a regularized least-squares estimator that jointly minimizes residuals of the steady-state mean and covariance equations across observational and interventional data. Experimental results validate our theoretical findings in recovering parameters of the underlying OU process.

Saber Salehkaleybar

Leiden Institute of Advanced Computer Science, Leiden University, The Netherlands

Parameter Estimation Stochastic Differential Equations Stochastic Linear Dynamical Systems Parameter Identifiability Causal Identifiability System Identification

Sep 10, 2026cs.LG

Generalised Score Matching on Convex Domains

Score matching avoids computing the normalising constant that maximum-likelihood estimation requires. On constrained domains, its generalised variants weight the Fisher divergence so that boundary terms vanish. We derive generalised score matching on open convex subsets of

\mathbb{R}^{d}

as the small-neighbourhood limit of minimum probability flow, in which the geometry of the neighbourhoods determines the weight. Every

C^{2}

positive definite weight arises in this way, including those of classical score matching on

\mathbb{R}^{d}

and of its variants for non-negative data on

\mathbb{R}_{+}^{d}

. For exponential families, we extend the standard convexity, consistency and asymptotic normality results to every such weight and show that the estimator converges to the true parameter under certain boundary conditions. For a truncated Gaussian on a polytope and a Dirichlet distribution on the simplex, proposed estimators attain the lowest median error of all methods compared, in at least 42 of 50 ground-truth configurations.

Nishanth Shetty, Saisuchith Mahajan, Chandra Sekhar Seelamantula

Department of Electrical Engineering Indian Institute of Science, Bengaluru 560012

Score Matching Parameter Estimation

Sep 1, 2026cs.LG

DeSyR: A Decoupled Symbolic Recovery Framework with PINN-Guided Structure Search and Physics-Informed Coefficient Refinement

Recovering compact explicit solutions from neural approximations is challenging when imperfect teacher data guide symbolic topology search and coefficient estimation. We present DeSyR, a decoupled symbolic recovery framework for differential equations. A physics-informed neural network guides repeated searches to construct candidate topologies with provisional constants. Once a topology is fixed, its coefficients are refined solely from the governing equation and prescribed constraints, followed by gated selection and verification. For linear fixed-topology parameterizations, we characterize teacher-error inheritance and show that finite-weight mixed data--physics fitting retains an

O(β^{-1})

teacher-dependent contribution when the teacher error projects onto the model space. Under well-posedness, representability, zero-residual attainment, and discrete determinacy, physics-only refinement conditionally recovers exact coefficients; for nonlinear parameterizations, the corresponding guarantees are local. DeSyR is evaluated on 15 differential-equation problems across 18 configurations covering high-order, space--time, multidimensional, nonlinear, and coupled systems. A candidate-level audit yields a 99.23% convergence rate among free-parameter refits, while every selected refinement involving free coefficients converges. Configuration-level median refined relative

L_2

errors are

2.31\times10^{-14}

or lower. In same-topology comparisons, refinement reduces error by eight to fourteen orders of magnitude. These results show that an approximate neural teacher can guide topology discovery without imposing its error scale on final recovered coefficients, provided a target-capable topology is retained and physics-only refinement converges.

Pancheng Niu, Jun Guo, Qiaolin He +2

Chengdu University of Information Technology, College of Applied Mathematics, Chengdu, 610225, China · Sichuan University, School of Mathematics, Chengdu, 610065, China · Hong Kong Polytechnic University, Department of Computing, Hong Kong, 999077, China +1

Parameter Estimation Physics-Informed ML Symbolic Regression

Aug 11, 2026cs.LG

Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

Qiyao Zhou, Xujia Zhu, Pierre Joli +2

LMEE, UnivEvry, Université Paris-Saclay, Evry, France · L2S, Université Paris-Saclay, CNRS, CentraleSupéléc, Gif-sur-Yvette, France · CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France

Neural Surrogate Modeling Parameter Estimation PDE Surrogate Modeling Model Calibration Physics-Informed ML Variational Inference

Aug 6, 2026stat.ML

Scalable estimation of VARMA models

Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captures with a few parameters what a pure autoregression matches only with many lags. We introduce an estimation framework that removes this computational barrier: each optimization iteration is independent of the series length

T

. The framework combines a partial-autocorrelation reparametrization that guarantees stationarity and invertibility by construction, Gaussian priors on the reparametrized coefficients with separate scales for diagonal and off-diagonal entries, and losses that depend on the data only through fixed-size sufficient statistics, evaluated by a Parseval (Fourier) identity at near-linear cost in the truncation length. This yields two point estimators: a regularized least-squares fit and a covariance-marginalized maximum-a-posteriori estimator. We prove that both recover the infinite-autoregressive representation of the true process at a near-parametric rate in fixed dimension, so the truncation introduces no asymptotic bias. The same machinery extends, at the same leading cost, to seasonal dynamics, exogenous regressors (VARMAX), and rolling-window refits. Empirically, the estimators stay close to the oracle forecast error from

d=10

to

d=40

(where classical conditional MLE returns non-invertible fits whose forecasts diverge) and match or beat VAR, Bayesian-VAR, component-wise ARMA, and sparse-VARMA baselines on retail-demand, meteorological, and air-quality data. This brings likelihood-based VARMA estimation, at a per-iteration cost independent of the series length, to the problem sizes where practitioners have so far relied on VAR models.

Daniel Paulin, Victor Elvira

College of Computing & Data Science Nanyang Technological University Singapore · School of Mathematics University of Edinburgh Edinburgh, UK

Multivariate Time Series Forecasting Parameter Estimation

Aug 4, 2026cs.LG

Wrong Operator or Blind Design? A Reference-Free Diagnostic for Physics-Informed Coefficient Learning

Physics-informed neural networks and hybrid models infer PDE coefficients from noisy data. When a trained network returns one, no standard check says whether to trust it. We show what those checks report when the operator is wrong: one sensor aggregating several diffusion sources. On one parabolic benchmark at

2\%

noise, the in-domain error is

1.4

times the noise while the identified diffusivity settles

30\%

off. Every least-squares minimiser reaches that value, which drifts

27\%

across windows; the network, whose objective is composite, settles

1.3\%

away. The checks stay as silent when the design is blind to a rate of a richer operator, though the remedies are opposite. We develop a reference-free diagnostic, read in the physical parameter, not the weights, without retraining the network: an information-matrix test on the residuals, a heterogeneity statistic across window refits, and a Fisher-rank statistic on the design at the rates the single fit postulates. On the analytic head the specification test holds its pre-registered ceiling and rejects every misspecified replicate of both benchmark configurations, with a notch against a missing reaction term. The rank statistic is exactly zero only where the design is blind; a wrong operator confined to that mode leaves the specification test mute, and the rank statistic says so before any fit. The window reading exceeds its ceiling by one seed in thirty. A network frozen at its minimum returns the same verdicts; one stopped short rejects as a wrong operator would.

Eric Fock

PIMENT Laboratory, Universit´e de La R´eunion, Le Tampon 97430, La R´eunion, France

Parameter Estimation Parameter Identifiability Model Misspecification Physics-Informed ML PDE Inverse Problems

Aug 1, 2026eess.AS

Band-Count Dense Modal Estimation with Fixed-Frequency Differentiable Resonator Refinement

Task B of the 1st DAFx Parameter Estimation Challenge requires estimating the frequencies, decay rates, gains, and number of modes in a dense plate-reverb impulse response. Weak and overlapping modes make sparse peak detection prone to severe undercounting. We train an ExtraTrees regressor on simulator-generated data to predict mode counts in four frequency bands. These counts define dense frequency grids, after which a differentiable all-pole resonator model refines decay and gain while keeping frequency fixed. On two separate synthetic validation sets, the system reduces a local challenge-style error by about 66% relative to the official default peak-picking baseline. The improvement is mainly associated with lower mode-count mismatch, while decay and gain remain the largest error sources. These findings support separating modal-density estimation from continuous parameter fitting.

Minhui Lu, Joshua D. Reiss

Centre for Digital Music Queen Mary University of London London, United Kingdom

Parameter Estimation

Aug 1, 2026eess.AS

Simulation-Based Plate-Reverb Parameter Estimation from a Single Impulse Response

We present a simulation-trained, non-iterative estimator for Task A of the 1st DAFx Parameter Estimation Challenge. Each unnormalized plate-reverb impulse response is summarized by amplitude, spectral, and decay descriptors, and an ensemble of tree regressors estimates the six target parameters in one pass. Across two independent synthetic validation sets, the normalized models outperform the training-set mean and an earlier raw-regression baseline. On a shared set, the final ensemble also outperforms a single run of the official default PSO at substantially lower inference cost. Since the official labels are hidden, parameter accuracy is measured on simulator-matched data, and the released responses support only audio-side consistency checks. The estimator returns point estimates without uncertainty.

Minhui Lu, Joshua D. Reiss

Centre for Digital Music Queen Mary University of London London, United Kingdom

Parameter Estimation

Jul 27, 2026stat.ME

Simulation-based parameter estimation via a combination of embedded normalizing flows and implied empirical probabilities under moment restrictions

In this work, we present a simulation-based parameter estimation framework for a model defined by a computational simulation of a physical system. We specifically outline an estimation framework consisting of two closely-integrated steps that facilitate an overall end-to-end parameter estimation scheme. The first step involves utilizing an embedded normalizing flow which is used to transform the unknown complex distribution of the residual information into a simple base distribution corresponding to the transformed residual information. In the second step, an empirical-likelihood estimator, under moment restrictions, is utilized for imposing an indirect constrain on the base distribution, where such an instantiated task reasonably allows us to treat the transformed residual information as random variables arising from discretely distribution population with each transformed data point as a single-cell from a set of finite-cell contingencies. Moreover, we use first-order gradient methods for updating the estimated parameter values of the model defined by the computational simulation and the corresponding parametrized embedded normalizing flow, that call for all gradient-related information by leveraging implicitly differentiations of the empirical-likelihood function, which is constructed from the implied empirical probabilities under moment restrictions. Here, it is worth mentioning that the problem formulation presented in this work, which highlights an information-theoretic interpretation, allows to present a computational framework for algorithmic implementations. Finally, as a-by-product, the inverse of the parametrized embedded normalizing flow, w.r.t. the estimated parameter values, serves as a surrogate model for the computational simulation model, which provides useful information for quantifying model discrepancies and sensitivity analysis.

Getachew K. Befekadu

DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING, COLLEGE OF ENGINEERING, PHYSICS, AND COMPUTING, THE CATHOLIC UNIVERSITY OF AMERICA, WASHINGTON, DC 20064, USA.

Simulation-Based Inference Parameter Estimation

Jul 23, 2026stat.ML

Simulation-Based Empirical Bayes

Empirical Bayes (EB) performs simultaneous inference across many related latent variables. Classical EB assumes that the likelihood p(x | z) is tractable. In many scientific applications, however, the likelihood is available only through a simulator. This paper develops EB for such implicit likelihoods. We introduce simulation-based empirical Bayes (SBEB), which connects nonparametric EB to simulation-based inference (SBI). SBEB computes EB estimates without an explicit density by using the observed data, simulator samples, and an amortized inference network. SBEB iteratively refines the fitted EB prior toward the population prior. With several scientific simulators and real-world data, we demonstrate that SBEB improves accuracy over SBI with a fixed prior.

Xinwei Shen, Diana Cai, Cheng Zhang +1

Department of Statistics University of Washington · Department of Computer Science Cornell University · School of Mathematical Sciences and Center for Statistical Science Peking University +1

Simulation-Based Inference Parameter Estimation Empirical Bayes

Jul 23, 2026cs.LG

An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning

Simulation-based inference (SBI) with machine learning is an increasingly important tool for solving inverse problems in science and engineering, including parameter inference and the inversion of detector effects. We provide an overview of the Bayesian and frequentist statistical frameworks, describe how machine-learning-based SBI methods, such as neural posterior estimation and neural likelihood estimation, can be used for parameter estimation within these frameworks, and show that the same methods can also be applied to Empirical Bayes or unfolding tasks. We also discuss how to validate inference results and the limitations of SBI with machine learning.

Maximilian Dax, Theo Heimel, Gilles Louppe

ELLIS Institute Tübingen, Max Planck Institute for Intelligent Systems, Tübingen AI Center, Tübingen, Germany · CP3, Université catholique de Louvain, Louvain-la-Neuve, Belgium · Montefiore Institute, University of Liège, Belgium

Simulation-Based Inference Parameter Estimation Neural Posterior Estimation Bayesian Inference

Jul 22, 2026cs.SD

Black-Box Optimization for Identifying and Inverting Audio Dynamic Range Control Effects

Dynamic Range Compression (DRC) is a widely used nonlinear audio effect whose parameters are often unknown, making blind estimation and inversion challenging. In this work, we formulate DRC parameter estimation as a black-box optimization problem in a perceptually motivated feature space. Given an observed signal and a reference representation, we estimate the parameters that minimize the distance between feature descriptors of the reconstructed and reference signals. Unlike gradient-based approaches, the proposed method does not require differentiability of the DRC model or the feature extraction pipeline, enabling the use of nonlinear and histogram-based descriptors. Experimental results demonstrate that the proposed method achieves competitive performance in blind parameter estimation and dry signal recovery, outperforming or matching state-of-the-art models in terms of reconstruction quality.

Haoran Sun, Dominique Fourer, Hichem Maaref

IBISC (EA 4526), Univ. Évry Paris-Saclay

Parameter Estimation

Jul 20, 2026cs.LG

Program Synthesis for Simulation-Based Inference: Joint Model Selection and Parameter Estimation

Neural simulation-based inference enables parameter estimation for complex models, but typically requires the user to specify a simulator encoding a fixed model structure. We present a framework for joint model selection and parameter estimation that combines large language models for program synthesis with neural simulation-based inference. Given a natural language description of the system and data under investigation, an LLM proposes candidate simulator programs which are iteratively refined via feedback-driven mutation and evaluated using neural density estimation. The approach enables simulation-based inference over a pool of models, not just parameters within a fixed model. On benchmarks spanning deterministic dynamics, stochastic epidemic models, and dark matter substructure inference from gravitational-lensing images, the method identifies plausible model families from open-ended prompts, with accuracy that reflects the information content of the data and identifiability of candidate models.

Siddharth Mishra-Sharma

Faculty of Computing & Data Sciences Boston University · Boston University

Simulation-Based Inference Parameter Estimation Bayesian Inference LLM-Based Program Synthesis

Jul 17, 2026cs.LG

Agentic Calibration of Grey-Box Simulation Models: An LLM-Driven Alternative

Calibration of grey-box simulation models is a constrained optimization problem in which model evaluations are expensive, the parameter space can be high-dimensional, and the search must respect plausibility constraints. Although the simulation code is fully available to the analyst, the joint effect of multiple parameters remains difficult to predict analytically. Classical optimizers such as Nelder--Mead (NM) are simple to deploy but sample-inefficient, particularly under constraints. Modern Bayesian Optimization methods achieve competitive solutions with far fewer evaluations but require non-trivial modeling machinery for constraint handling. We introduce an agentic calibration method in which a large language model acts as the optimizer, with constraints incorporated as a plain-language section of the system prompt. We evaluate the agentic method, NM, and Bayesian Optimization (BO) on an anal cancer simulation model under both unconstrained and clinically constrained calibration. Under unconstrained calibration, the agentic method achieves substantially lower best error than BO and NM, while requiring fewer model evaluations. Under constrained calibration, the agentic method reaches comparable error levels and both outperform NM. These results are obtained at the cost of increased inference time per iteration. Agentic calibration achieves competitive performance with substantially fewer model evaluations, and constraint handling is essentially free at the modeller-facing interface through simple textual specifications rather than additional modelling machinery. The main trade-off lies in increased per-iteration inference cost, making the approach particularly suitable when simulation time dominates. Beyond performance, the per-iteration rationale makes the search auditable and explainable, so its decisions can be scrutinised and justified to third parties.

David Gómez-Guillén, Mireia Diaz, Josep Lluis Arcos +1

Unit of Infections and Cancer – Information and Interventions (UNIC-I&I), Cancer Epidemiology Research Program, Catalan Institute of Oncology-IDIBELL, L’Hospitalet de Llobregat, Spain · Autonomous University of Barcelona (UAB), Spain · Centro de Investigación Biomédica en Red de Epidemiología y Salud Pública (CIBERESP), Ministerio de Ciencia, Innovación y Universidades, Madrid, Spain +1

Parameter Estimation Black-Box Optimization Large Language Model-Guided Optimization Model Calibration Constrained Optimization

Jul 16, 2026cs.LG

RTS Smoother-Guided Learning of Physics-Based Neural Differential Models

Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured. We propose a hybrid neural--physics framework in which the known components of the ODE are kept explicit and the missing components are represented by a neural network. The proposed method consists of two stages where we alternate between state and parameter estimation and iterate until a predetermined criterion is met. Specifically, in the first step, we treat the model parameters as being known and we infer the latent states from the available measurements using a Rauch--Tung--Striebel (RTS) smoother. In the second stage, we treat the smoothed trajectories as being known and use them to estimate the neural networks' parameters through backpropagation. We evaluate the method on benchmark systems spanning linear, nonlinear, and stiff dynamics under partial state observation. Across these settings, the proposed method learns missing ODE components from incomplete measurements while exploiting and retaining interpretable mechanistic structure and improving latent-state reconstruction and long-horizon prediction.

Ahmet Demirkaya, Georgios Stratis, Tales Imbiriba +2

Department of Electrical and Computer Engineering Northeastern University · Department of Computer Science University of Massachusetts Boston · Emory University

Dynamical Systems Parameter Estimation Latent Dynamics Modeling Nonlinear System Identification Physics-Informed ML Neural ODEs

Jul 14, 2026hep-ph

Physically Consistent Parameter Inference: Transparent Machine Learning Emulation in High Energy Physics and Cosmology

Global fits in high energy physics and cosmology often face the challenge of exploring high-dimensional parameter spaces with computationally expensive or topologically complex likelihood functions. In this work, we present a Machine Learning framework designed to emulate complex, often non-Gaussian likelihood landscapes using gradient-boosted regression trees (XGBoost). We discuss the advantages of the Machine Learning approach in terms of computational efficiency and the resolution of confidence regions, particularly in scenarios with complex correlations or "curved" degeneracies. We validate this methodology by applying it to a recent analysis on flavour anomalies in semileptonic

B

meson decays and discussing the adaptability of this framework to other phenomenological systems, such as axion-like particles or cosmology global fits. Finally, we utilise SHAP (Shapley Additive exPlanations) values to provide a transparent analysis of feature importance, ensuring that the Machine Learning predictions remain physically interpretable and consistent with the underlying physics.

Jorge Alda, Jacobo Asorey, Alejandro Mir +1

Dipartimento di Fisica e Astronomia “Galileo Galilei”, Universit`a degli Studi di Padova & INFN Sezione di Padova, via Marzolo 8, 35131 Padova, Italy · Centro de Astropart´ıculas y F´ısica de Altas Energ´ıas (CAPA), Pedro Cerbuna 12 50009 Zaragoza, Spain · Departamento de F´ısica Te´orica, Facultad de Ciencias, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain

Parameter Estimation High-Energy Physics

Jul 13, 2026cs.LG

NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process

In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are developed to estimate the model parameters

(μ,γ,α,β)

directly from sequences of inter-arrival times without requiring computationally intensive likelihood optimization. Experiments on synthetic data that both neural models significantly outperform the classical Maximum Likelihood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy (MSE =

0.1634

), followed by the LSTM (MSE =

0.1752

), compared to MLE (MSE =

2.8032

). An ablation study further examines the effects of key hyperparameters on model performance. The proposed framework is also on two real-world high-frequency datasets, namely AAPL NBBO transaction data and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the estimated parameters closely reproduce the empirical distribution, tail behavior, and temporal dependence structure of the observed data. These results demonstrate that Transformer-based parameter estimation provides an accurate and efficient alternative to conventional estimation techniques for FHP and offers a promising framework for modeling event-driven systems with long-memory dynamics.

Neha Gupta, Aditya Maheshwari

Operations Management and Quantitative Techniques Area, Indian Institute of Management Indore, Indore 453556, India.

Temporal Point Processes Parameter Estimation

Jul 12, 2026stat.ML

Representation Learning for Semiparametric Causal Mediation Analysis under No Essential Heterogeneity

We propose a two-stage estimator for structural mediation parameters that combines deep representation learning with G-estimation under the "no essential heterogeneity" (NEH) assumption. We call the method UNIT. In the first stage,TARNet estimates the heterogeneous effect of a randomized treatment on a mediator by learning a shared covariate representation across treatment arms.The resulting conditional average treatment effect (CATE) estimate provides a plug-in approximation to the heterogeneity-dependent component of the weight function entering the G-estimating equation of Zheng and Zhou (2015), which identifies the structural parameters even in the presence of unmeasured mediator-outcome confounding. We show that more accurate first-stage representation learning can yield a more informative plug-in weight and thereby improve the precision of the structural parameter estimator. In simulations with non-Gaussian covariates and nonlinear mediator effects, TARNet weights reduce the Stage-2 standard error of the mediation coefficient by a factor of

1.45

to

1.51

(median across replications,

n \ge 2000

) relative to the classical approach, at no cost to bias or coverage.

Roberto Faleh, Sofia Morelli, Holger Brandt

Methods Center University of Tübingen, Germany

Semiparametric Inference Parameter Estimation Causal Effect Estimation Causal Mediation Analysis

Jul 8, 2026econ.EM

Sensitivity to Subjective Expected Utility Maximization: A Methodological Study, with an Illustrative Application to LLM Decision-Making

Evaluating decisions made under uncertainty is hard when labeled outcomes are scarce, costly, or confounded with luck. We treat subjective expected utility (SEU) maximization as a stated standard and define a graded measure -- SEU sensitivity -- of an agent's conformity to it. The vehicle is a softmax choice model with a sensitivity parameter

α

on SEU-valued alternatives; the contribution is a sequence of identifiability results for

α

and for belief and utility parameters

(β, δ)

, validated in Stan via prior predictive checks, parameter recovery, and simulation-based calibration (SBC), with finite-sample caveats intact. In the uncertain-choice-only model

m_0

,

α

is identifiable given the expected-utility vector

η

and sharply recovered, while

(β, δ)

are only weakly informed: the posterior barely contracts and concentrates on a

β

-

δ

trade-off. In the extended model

m_1

,

δ

becomes identifiable in principle via a

β

-free risky block, but its practical recovery gain at realistic sample sizes is negligible (matched-count CI-width reduction under 1%), and that block yields no detected

α

-precision gain at matched choice count. These are two distinct phenomena: for

δ

, identifiability does not imply precise estimability at realistic

n

; for

α

, identifiability is silent about what governs finite-

n

precision. Marginal SBC passes for both models even where the joint posterior is weakly informed -- a demarcation we make precise. A two-by-two application (GPT-4o and Claude 3.5 Sonnet, each on insurance-claims triage and Ellsberg-style urns, with sampling temperature as the lever) runs end-to-end on real LLM choice data, detecting a structured comparative

α

effect in two of four cells.

Jeff Helzner

Parameter Estimation Parameter Identifiability Discrete Choice Modeling Decision-Making under Uncertainty

Jul 7, 2026stat.ML

The Regularization Parameter: Sparse Precision Matrix Estimation

Sparse precision matrix estimation provides an interpretable and computationally efficient framework for modeling conditional dependencies in high-dimensional, low-sample-size data. A recurring challenge is appropriately selecting the regularization parameter that controls estimator sparsity and strikes a balance between underfitting and overfitting. We propose a closed-form, matrix-valued regularization parameter derived from the sampling distribution of the first-order optimality conditions of the

\ell_1

-regularized Gaussian maximum-likelihood estimator. By prescribing the probability that each nonzero entry of the estimator satisfies its optimality condition under resampling, we eliminate the need for cross-validation. The resulting regularization parameter is shown to attain asymptotic scaling properties that, under standard conditions, provide consistency and sparsistency of the estimator. On synthetic Gaussian and non-Gaussian datasets, as well as real-world gene microarray and neuroimaging applications, the proposed approach achieves estimation accuracy comparable to cross-validation, delivers superior support recovery, and reduces runtime by several orders of magnitude.

Aryan Eftekhari, Daniel Sergio Vega, Ernst-Jan Camiel Wit +1

Institute of Computing, Faculty of Informatics, Universit`a della Svizzera italiana (USI), Lugano, Switzerland

Graph Structure Learning Parameter Estimation Sparse Recovery Hyperparameter Optimization