Self-Supervised Calibration of Scientific Instruments Using Physical Consistency Constraints

Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems. We introduce Amortized Physics-Informed Calibration (APIC), a population-level extension of KOH that leverages Neural Processes to perform scalable Bayesian inference across realizations. Our framework employs a two-branch latent architecture to disentangle instance-specific physical parameters from shared, state-dependent structural discrepancies. By integrating differentiable physics into an amortized inference backbone, APIC enables rapid calibration of unseen realizations from sparse observations while quantifying uncertainty. Experiments on the damped spring oscillator, the Lotka-Volterra system, and the advection-diffusion PDE with misspecified physics demonstrate improved parameter recovery and consistent identification of the systemic discrepancy structure compared to other calibration approaches.

Data augmentations define the invariances learned by self-supervised learning (SSL). Standard augmentation pipelines were designed for natural images, yet scientific imaging modalities are governed by physical measurement processes with distinct symmetry and acquisition constraints. Enforcing invariances that contradict these constraints can distort learned representations and limit downstream performance, but practitioners moving from machine learning into a new scientific modality currently have little guidance beyond transferring natural-image pipelines unexamined. We address this gap with a principled, reproducible procedure for augmentation design in scientific SSL: we formalise the physics-aligned augmentation set as a union of measurement-consistent symmetries and acquisition-driven perturbations, and we give a concrete, largely label-free workflow---enumerate candidates, label each by the measurement operator, validate with representation-geometry diagnostics, and confirm by single-factor ablation---for selecting them. We instantiate the procedure for real-space electron microscopy and reciprocal-space 4D-STEM diffraction, and evaluate it across five SSL paradigms (DINOv2, SimCLR, MAE, VICRegL, I-JEPA) on classification and crystal-orientation regression. Physics-aligned augmentations substantially improve downstream performance for objectives relying on cross-view consistency, reduce geodesic error and improve robustness under realistic acquisition variability (detector gain, resolution loss), and systematically reshape representation geometry. While our experiments use electron microscopy, the procedure is modality-agnostic and applies to other measurement-driven domains such as medical and remote-sensing imaging. These results position augmentation design as a primary, and controllable, source of inductive bias in scientific self-supervised learning.

Deep neural networks have become a promising approach for IMU-based sensing, but their scalability is fundamentally limited by costly labeled data and poor robustness to heterogeneous devices, placements, and users. Existing unsupervised and self-supervised methods reduce but do not remove this dependence, still requiring labeled data for domain adaptation and largely ignoring known physical structure. We propose physical self-supervised learning, an autoencoder-style paradigm for label-free IMU sensing. We replace the conventional neural decoder with an auto-adaptive physics decoder, a learnable family of kinematic equations that enforces explicit physical structure while adapting across environments, and adopt a hybrid two-stage IMU encoder with reconstruction in a structured latent space to mitigate sensor noise. Our framework further introduces probabilistic frequency-spatial constraints to disentangle sensor and object motion, a multi-view kinematic tree to exploit sparse physical self-supervised signals, and an uncertainty-aware formulation to handle the inherent ambiguity of IMU inference. Evaluated on inertial tracking and full-body motion capture over public datasets and realistic deployments, physical self-supervised learning reduces errors by up to 5x for tracking and 4x for motion capture in challenging generalization scenarios, consistently outperforming state-of-the-art supervised and self-supervised baselines without any labels. Our code is available at https://github.com/YuyangLeng/physical-ssl-imu-label-free