Precise pose estimation of optical microrobots is essential for enabling high-precision object tracking and autonomous biological studies. However, current methods rely heavily on large, high-quality microscope image datasets, which are difficult and costly to acquire due to the complexity of microrobot fabrication and the labour-intensive labelling. Digital twin systems offer a promising path for sim-to-real data augmentation, yet existing techniques struggle to replicate complex optical microscopy phenomena, such as diffraction artifacts and depth-dependent imaging.This work proposes a novel physics-informed deep generative learning framework that, for the first time, integrates wave optics-based physical rendering and depth alignment into a generative adversarial network (GAN), to synthesise high-fidelity microscope images for microrobot pose estimation efficiently. Our method improves the structural similarity index (SSIM) by 35.6% compared to purely AI-driven methods, while maintaining real-time rendering speeds (0.022 s/frame).The pose estimator (CNN backbone) trained on our synthetic data achieves 93.9%/91.9% (pitch/roll) accuracy, just 5.0%/5.4% (pitch/roll) below that of an estimator trained exclusively on real data. Furthermore, our framework generalises to unseen poses, enabling data augmentation and robust pose estimation for novel microrobot configurations without additional training data.

In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems -- especially in aerospace -- this region cannot be determined a priori and is often challenging to compute. One of the most common methods for computing the stability region is to identify a Lyapunov function. A Lyapunov function is a positive function whose time derivative along system trajectories is non-positive, which provides a sufficient condition for stability and characterizes an estimated stability region. However, existing methods of characterizing a stability region via a Lyapunov function often rely on explicit knowledge of the system governing equations. In this work, we present a new physics-informed machine learning method of characterizing an estimated stability region by inferring a Lyapunov function from system trajectory data that treats the dynamical system as a black box and does not require explicit knowledge of the system governing equations. In our presented Lyapunov function Inference method (LyapInf), we propose a quadratic form for the unknown Lyapunov function and fit the unknown quadratic operator to system trajectory data by minimizing the average residual of the Zubov equation, a first-order partial differential equation whose solution yields a Lyapunov function. The inferred quadratic Lyapunov function can then characterize an ellipsoidal estimate of the stability region. Numerical results on benchmark examples demonstrate that our physics-informed stability analysis method successfully characterizes a near-maximal ellipsoid of the system stability region associated with the inferred Lyapunov function without requiring knowledge of the system governing equations.

Optical microrobots actuated by optical tweezers (OT) offer great potential for biomedical applications such as cell manipulation and microscale assembly. These tasks demand accurate three-dimensional perception to ensure precise control in complex and dynamic biological environments. However, the transparent nature of microrobots and low-contrast microscopic imaging challenge conventional deep learning methods, which also require large annotated datasets that are costly to obtain. To address these challenges, we propose a physics-informed, data-efficient framework for depth estimation of optical microrobots. Our method augments convolutional feature extraction with physics-based focus metrics, such as entropy, Laplacian of Gaussian, and gradient sharpness, calculated using an adaptive grid strategy. This approach allocates finer grids over microrobot regions and coarser grids over background areas, enhancing depth sensitivity while reducing computational complexity. We evaluate our framework on multiple microrobot types and demonstrate significant improvements over baseline models. Specifically, our approach reduces mean squared error (MSE) by over 60% and improves the coefficient of determination (R^2) across all test cases. Notably, even when trained on only 20% of the available data, our model outperforms ResNet50 trained on the full dataset, highlighting its robustness under limited data conditions. Our code is available at: https://github.com/LannWei/CBS2025.

Compared to physics-based computational manufacturing, data-driven models such as machine learning (ML) are alternative approaches to achieve smart manufacturing. However, the data-driven ML's "black box" nature has presented a challenge to interpreting its outcomes. On the other hand, governing physical laws are not effectively utilized to develop data-efficient ML algorithms. To leverage the advantages of ML and physical laws of advanced manufacturing, this paper focuses on the development of a physics-informed machine learning (PIML) model by integrating neural networks and physical laws to improve model accuracy, transparency, and generalization with case studies in laser metal deposition (LMD).

The mass loss of the polar ice sheets contributes considerably to ongoing sea-level rise and changing ocean circulation, leading to coastal flooding and risking the homes and livelihoods of tens of millions of people globally. To address the complex problem of ice behavior, physical models and data-driven models have been proposed in the literature. Although traditional physical models can guarantee physically meaningful results, they have limitations in producing high-resolution results. On the other hand, data-driven approaches require large amounts of high-quality and labeled data, which is rarely available in the polar regions. Hence, as a promising framework that leverages the advantages of physical models and data-driven methods, physics-informed machine learning (PIML) has been widely studied in recent years. In this paper, we review the existing algorithms of PIML, provide our own taxonomy based on the methods of combining physics and data-driven approaches, and analyze the advantages of PIML in the aspects of accuracy and efficiency. Further, our survey discusses some current challenges and highlights future opportunities, including PIML on sea ice studies, PIML with different combination methods and backbone networks, and neural operator methods.

We present a physics-informed machine-learning (PIML) approach for the approximation of slow invariant manifolds (SIMs) of singularly perturbed systems, providing functionals in an explicit form that facilitate the construction and numerical integration of reduced order models (ROMs). The proposed scheme solves a partial differential equation corresponding to the invariance equation (IE) within the Geometric Singular Perturbation Theory (GSPT) framework. For the solution of the IE, we used two neural network structures, namely feedforward neural networks (FNNs), and random projection neural networks (RPNNs), with symbolic differentiation for the computation of the gradients required for the learning process. The efficiency of our PIML method is assessed via three benchmark problems, namely the Michaelis-Menten, the target mediated drug disposition reaction mechanism, and the 3D Sel'kov model. We show that the proposed PIML scheme provides approximations, of equivalent or even higher accuracy, than those provided by other traditional GSPT-based methods, and importantly, for any practical purposes, it is not affected by the magnitude of the perturbation parameter. This is of particular importance, as there are many systems for which the gap between the fast and slow timescales is not that big, but still ROMs can be constructed. A comparison of the computational costs between symbolic, automatic and numerical approximation of the required derivatives in the learning process is also provided.

In this paper, we present a physics-informed neural network (PINN) approach for predicting the performance of an all-vanadium redox flow battery, with its physics constraints enforced by a two-dimensional (2D) mathematical model. The 2D model, which includes 6 governing equations and 24 boundary conditions, provides a detailed representation of the electrochemical reactions, mass transport and hydrodynamics occurring inside the redox flow battery. To solve the 2D model with the PINN approach, a composite neural network is employed to approximate species concentration and potentials; the input and output are normalized according to prior knowledge of the battery system; the governing equations and boundary conditions are first scaled to an order of magnitude around 1, and then further balanced with a self-weighting method. Our numerical results show that the PINN is able to predict cell voltage correctly, but the prediction of potentials shows a constant-like shift. To fix the shift, the PINN is enhanced by further constrains derived from the current collector boundary. Finally, we show that the enhanced PINN can be even further improved if a small number of labeled data is available.

The Ornstein-Zernike (OZ) equation is the fundamental equation for pair correlation function computations in the modern integral equation theory for liquids. In this work, machine learning models, notably physics-informed neural networks and physics-informed neural operator networks, are explored to solve the OZ equation. The physics-informed machine learning models demonstrate great accuracy and high efficiency in solving the forward and inverse OZ problems of various bulk fluids. The results highlight the significant potential of physics-informed machine learning for applications in thermodynamic state theory.

Well-calibrated traffic flow models are fundamental to understanding traffic phenomena and designing control strategies. Traditional calibration has been developed base on optimization methods. In this paper, we propose a novel physics-informed, learning-based calibration approach that achieves performances comparable to and even better than those of optimization-based methods. To this end, we combine the classical deep autoencoder, an unsupervised machine learning model consisting of one encoder and one decoder, with traffic flow models. Our approach informs the decoder of the physical traffic flow models and thus induces the encoder to yield reasonable traffic parameters given flow and speed measurements. We also introduce the denoising autoencoder into our method so that it can handles not only with normal data but also with corrupted data with missing values. We verified our approach with a case study of I-210 E in California.

Anima Anandkumar, NVIDIA's senior director of machine learning research, and Karthik Kashinath, NVIDIA's AI and HPC engineering lead, will cover how the company's Earth-2 supercomputer will improve predictions of extreme weather events and accelerate effective climate-change mitigation using physics-informed machine learning and digital twin simulation. Tab Tang, president of the general-purpose server field at xFusion Digital Technologies, will present how low-carbon computing power can be used to power data centers, resulting in high efficiency and energy savings for the digital economy. Edoardo Nemni, data scientist at the United Nations Satellite Centre; Alison Lowndes, principal scientist at NVIDIA; and Shilpa Kolhatkar, global head of AI nations business development at NVIDIA, will discuss how AI and deep learning can be used for real-time monitoring of Earth with geospatial satellite imagery -- to predict and respond to natural disasters, as well as manage energy sources. Dirk Van Essendelft, William Epting and Tarak Nandi from the National Technology Laboratory, will highlight how physics-machine learning technology powered by the NVIDIA Modulus framework and Omniverse simulation platform can help the lab reach its zero-carbon emission target. Anima Anandkumar, NVIDIA's senior director of machine learning research, and Karthik Kashinath, NVIDIA's AI and HPC engineering lead, will cover how the company's Earth-2 supercomputer will improve predictions of extreme weather events and accelerate effective climate-change mitigation using physics-informed machine learning and digital twin simulation.