physics-informed inference

This study addresses the challenge of jointly modeling calibration and control parameters in computer model calibration, where the distribution of calibration parameters is unknown while that of control parameters is known. To tackle this issue, the authors propose a nonparametric Bayesian calibration method based on measure decomposition. The approach preserves the known marginal distribution of the control parameters while employing stochastic process modeling and Bayesian inference to construct a posterior distribution over the input space that aligns with field observations. Notably, this work is the first within a nonparametric calibration framework to explicitly maintain the prior distributional properties of the control parameters, thereby substantially enhancing the physical consistency and scientific credibility of the calibration results.

In physical modeling, conventional Gaussian random fields (GRFs) fail to rigorously satisfy prescribed linear boundary constraints—such as fixed values (Dirichlet), fixed derivatives (Neumann), or mixed-type (Robin) conditions—leading to priors inconsistent with underlying physical laws. To address this, we propose the first general framework for constructing GRFs on multidimensional convex domains that *exactly* satisfy arbitrary-order continuous linear boundary constraints. Our method leverages orthogonal projection in function spaces combined with linear differential operator constraints to map an unconstrained GRF onto the subspace of functions adhering to the specified boundary conditions. This yields analytically exact enforcement of Dirichlet, Neumann, and Robin constraints—unprecedented in prior GRF constructions—and delivers physically consistent probabilistic priors. Experiments demonstrate substantial improvements in predictive accuracy and calibrated uncertainty quantification across applications including probabilistic numerical solving of PDEs, dynamical system discovery, and boundary-aware state estimation.

In data assimilation, uncertainty quantification remains challenging due to the coupling of dynamical models with process noise and sparse, noisy observations. To address this, we propose a variational inference–based uncertainty-aware data assimilation framework that models stochastic state evolution as a multivariate Gaussian distribution, enabling approximately perfectly calibrated uncertainty estimates and supporting longer assimilation windows. The method is end-to-end differentiable and seamlessly embeddable within machine learning architectures. Evaluated on the chaotic Lorenz-96 system, it achieves high state estimation accuracy while significantly improving uncertainty calibration and out-of-distribution generalization compared to conventional approaches. All code is publicly available to facilitate reproducibility and further research extensions.

This work addresses the challenge of accurately estimating the filtering distribution (i.e., the state posterior) in high-dimensional nonlinear dynamical systems. To overcome the bias inherent in traditional ensemble Kalman filters (EnKF) under strong nonlinearity and their reliance on labor-intensive manual tuning, we propose an end-to-end learning framework grounded in variational inference. Specifically, the filter’s analysis step is modeled as a learnable, parameterized analysis mapping; key components—including gain computation, covariance inflation, and localization—are jointly optimized via a variational objective. This constitutes the first systematic integration of variational inference into filter design, enabling unified modeling and automatic calibration of the analysis process. Experiments across diverse linear and nonlinear systems demonstrate that our method significantly reduces filtering bias, improves posterior estimation accuracy, and drastically diminishes dependence on manual parameter tuning.

This work addresses trajectory tracking control for linear time-invariant (LTI) systems. We propose a physics-informed Gaussian process (GP) model predictive control (MPC) framework. Methodologically, we embed the LTI system’s constant-coefficient linear differential equation as a hard constraint into the GP prior—enabling “control-as-inference”—and introduce a virtual setpoint mechanism to explicitly encode and enforce pointwise soft constraints. Theoretically, we prove asymptotic stability of the resulting closed-loop system under the optimal control law. Numerical experiments demonstrate superior constraint satisfaction, tracking accuracy, and robustness compared to baseline methods. Our approach establishes a new paradigm for data-driven control that unifies physical interpretability—through first-principles differential equation constraints—with rigorous stability guarantees.

This study systematically characterizes the diversity and complexity of parametric Bayesian inference problems in astronomy, cosmology, and particle physics. By leveraging both real and simulated data, it constructs the first cross-disciplinary framework for Bayesian inference problem spaces, structured along seven dimensions—including parameter dimensionality, posterior geometry, information content, and multimodality—and establishes a standardized benchmark suite. Employing parametric inference methods, posterior analysis, and Dockerized computational environments, the work reveals that astrophysical inference tasks span the full spectrum from low- to high-dimensional settings, unimodal to multimodal posteriors, and weakly to strongly informative regimes. The resulting platform offers a reproducible and extensible infrastructure for rigorous evaluation and comparison of Bayesian inference methodologies across scientific domains.

In signal detection tasks within physical sciences and related fields, background interference is often unknown and highly complex. This work proposes a geometrically motivated, single-parameter approach termed the “compensator,” which enables effective inference of signal strength without requiring a full model of the background distribution. Grounded in geometric analysis and statistical inference, the method operates within a likelihood-based framework, substantially reducing computational complexity while naturally accounting for the source of inferential conservatism. The resulting detection mechanism is both more parsimonious and robust, offering a principled means to quantify the reliability of inferences under background uncertainty.

This study addresses the limitation that single observation mode evaluations fail to capture performance fluctuations in physical field reconstruction by proposing an integrated benchmark platform. The platform incorporates seven types of partial differential equation data with configurable observation operators, enabling parameterized mode definitions through the decoupling of observation construction from physical records, and establishes a standardized cross-mode evaluation protocol to quantify model sensitivity. Experiments reveal that cross-mode errors consistently exceed matched-mode errors, and dense observations do not necessarily reduce errors. Furthermore, mixed training strategies effectively mitigate transfer errors. This work provides a systematic tool and novel insights for the robustness evaluation of physical field reconstruction.

This work addresses the challenge of signal detection in high-dimensional binned Poisson count data with unknown background by extending the compensator inference framework—originally developed for unbinned settings—to the binned data context for the first time. By introducing a single compensator parameter within a mixture model to govern inference conservativeness, the method circumvents the need for direct estimation of potentially misspecified background component densities. Consequently, it achieves robust signal detection without explicitly modeling the background distribution, effectively controlling the false positive rate while enhancing detection power. This approach offers a computationally efficient and statistically reliable solution for identifying sparse signals in high-dimensional count data, with direct applicability to modern physics and astronomical experiments where background uncertainty is a critical concern.

This work addresses the challenge of constructing efficient surrogate models for parametrized systems in multi-query scenarios—such as optimization, control, and uncertainty quantification—by proposing a unified scientific machine learning framework that systematically integrates physics-driven, data-driven, and hybrid modeling paradigms. The framework encompasses techniques including Proper Orthogonal Decomposition (POD), Proper Generalized Decomposition (PGD), and neural networks, viewed through the lens of function approximation. A key innovation lies in unifying the selection of reduced-order bases and approximation criteria within a coherent analytical framework. Furthermore, the study explores emerging directions such as multi-fidelity fusion, adaptive sampling, and data augmentation. The resulting methodology offers both theoretical foundations and novel modeling paradigms with broad applicability in digital twins, smart manufacturing, and personalized medicine.