Physics-Informed Neural Networks (PINNs) represent a hybrid modeling paradigm that embeds governing physical laws, expressed as partial differential equations (PDEs), directly into neural network training. This integration enables models to respect fundamental conservation principles while learning from sparse or incomplete data. This review critically examines PINN applications in water and wastewater systems over the period 2014-2024, focusing on drinking water distribution networks, wastewater treatment plants, urban drainage systems, and water treatment processes. The review shows that PINNs excel in inverse problem solving by enabling parameter estimation and system identification from indirect observations, while maintaining physical consistency in extrapolation regimes where purely data-driven models fail. Documented applications report performance advantages, including 3-30 × reductions in required training data compared to standard neural networks, improved generalization under distribution shift, and successful use in scenarios involving partial observations and uncertain boundary conditions. However, critical limitations emerge: PINNs require well-posed problems with reliable governing equations, struggle with complex networked systems involving discrete components, face major convergence challenges for stiff or multi-scale PDEs, and still lack mature uncertainty quantification frameworks. Rather than positioning PINNs as replacements for established numerical methods, this work frames them as complementary tools that bridge mechanistic modeling and data-driven learning, offering particular value in parameter calibration, sensor placement optimization, and real-time state estimation for water infrastructure systems.

We learn parameterized nonlinear elasticity on curved surfaces using a physics-informed neural network that enforces governing equations and boundary conditions directly through the loss function, enabling a single trained model to represent a continuous family of elastic equilibria across geometric and material parameters. Nonlinear elasticity on curved manifolds underlies the mechanics of crystalline shells, elastic membranes, and viral capsids, where curvature and topological defects determine equilibrium structure and stability. Traditional exact and finite element solvers rely on symmetry reduction and must be reinitialized for each parameter choice, limiting scalability when symmetry is broken or parameters vary. We validate the proposed learning-based solver on a benchmark problem from curved elasticity, namely the one-dimensional single disclination on a spheroidal surface with known exact and numerical solutions. The network accurately reproduces these solutions, including parameter combinations excluded from training, demonstrating generalization across geometry and material regimes. This study establishes a scalable framework for learning nonlinear elastic systems on curved manifolds and lays the groundwork for extensions to fully two-dimensional and multi-defect configurations relevant to protein shells and other curved elastic networks.

We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through residual-based loss terms, NewPINNs integrates the solver directly into the training loop and defines learning objectives through solver-consistency. The neural network produces candidate solution states that are advanced by the numerical solver, and training minimizes the discrepancy between the network prediction and the solver-evolved state. This pull-push interaction enables the network to learn physically admissible solutions through repeated exposure to the solver's action, without requiring problem-specific loss engineering or explicit evaluation of differential equation residuals. By delegating the enforcement of physics, boundary conditions, and numerical stability to established numerical solvers, NewPINNs mitigates several well-known failure modes of standard physics-informed neural networks, including optimization pathologies, sensitivity to loss weighting, and poor performance in stiff or nonlinear regimes. We demonstrate the effectiveness of the proposed approach across multiple forward and inverse problems involving finite volume, finite element, and spectral solvers.

In this work, we present a test-driven, agentic framework for synthesizing a deployable low-level robot controller for navigation tasks. Given a 2D map with an image of an ultrasonic sensor-based robot, or a 3D robotic simulation environment, our framework iteratively refines the generated controller code using diagnostic feedback from structured test suites to achieve task success. We propose a dual-tier repair strategy to refine the generated code that alternates between prompt-level refinement and direct code editing. We evaluate the approach across 2D navigation tasks and 3D navigation in the Webots simulator. Experimental results show that test-driven synthesis substantially improves controller reliability and robustness over one-shot controller generation, especially when the initial prompt is underspecified. The source code and demonstration videos are available at: https://shivanshutripath.github.io/robotic_controller.github.io.

Accurate and rapid estimation of hemodynamic metrics, such as pressure and wall shear stress (WSS), is important for assessing the severity of Coronary Artery Disease (CAD). Existing approaches, including invasive Fractional Flow Reserve (FFR) measurements and computationally expensive Computational Fluid Dynamics (CFD) simulations, face challenges in invasiveness, cost, and speed. We present a framework for fast, non-invasive coronary hemodynamics prediction. The model encodes 1D vessel centerlines together with inlet flow rate using a transformer-based encoder, and predicts continuous wall-based fields via an anisotropic Radial Basis Function (RBF) decoder aligned with vessel morphology. To support training and evaluation, we introduce two datasets with paired steady-state OpenFOAM simulations: (i) a synthetic benchmark of 4,200 single-vessel geometries with controlled anatomical variations, and (ii) a multi-vessel dataset derived from ImageCAS including 4,800 cases spanning both right and left coronary arteries, generated by randomly introducing stenoses and varying physiologically plausible flow rates. Across both datasets, our method achieves lower pressure and WSS errors than strong neural-operator baselines (GNOT, Transolver, and ONO) at a fraction of the computational cost of CFD. On the multi-vessel dataset, using 1,024 anisotropic RBF centers our model reduces the mean relative L2 error by 52

More than 10 million coronary angiograms are performed globally each year, providing a gold standard for detecting obstructive coronary artery disease. Yet, no obstructive lesions are identified in 70

Sequential Model-Based Optimization (SMBO) is a highly effective strategy for hyperparameter search in machine learning. It utilizes a surrogate model that fits previous trials and approximates the hyperparameter response surface (performance). This surrogate model primarily guides the decision making process for selecting the next set of hyperparameters. Existing classic surrogates, such as Gaussian processes and random forests, focus solely on the current task of interest and cannot incorporate trials from historical tasks. This limitation hinders their efficacy in various applications. Inspired by the state-of-the-art convolutional neural process, this paper proposes a novel meta-learning-based surrogate model for efficient and effective hyperparameter optimization. Our surrogate is trained on the meta-knowledge from a range of historical tasks, enabling it to accurately predict the hyperparameter response surface even with a limited number of trials on a new task. We tested our approach on the hyperparameter selection problem for the well known support vector machine (SVM), residual neural network (ResNet), and vision transformer (ViT) across hundreds of real world classification datasets. The empirical results demonstrate its superiority over existing surrogate models, highlighting the effectiveness of meta-learning in hyperparameter optimization.

Optimizing the performance of deep neural networks (DNNs) remains a significant challenge due to the sensitivity of models to both hyperparameter selection and weight initialization. Existing approaches typically address these two factors independently, which often leads to limiting adaptability and overall effectiveness. In this paper, we present a novel meta-learning framework that jointly recommends hyperparameters and initial weights by leveraging dataset similarity. Our method begins by extracting meta-features from a collection of historical datasets. For a given query dataset, similarity is computed based on distances in the meta-feature space, and the most similar historical datasets are used to recommend the underlying parameter configurations. To capture the diverse characteristics of image datasets, we introduce two complementary types of meta-features. The first, referred to as shallow or visible meta-features, comprises five groups of statistical measures that summarize color and texture information. The second, termed deep or invisible meta-features, consists of 512 descriptors extracted from a convolutional neural network pre-trained on ImageNet. We evaluated our framework in 105 real-world image classification tasks, using 75 datasets for historical modeling and 30 for querying. Experimental results with both vision transformers and convolutional neural networks demonstrate that our approach consistently outperforms state-of-the-art baselines, underscoring the effectiveness of dataset-driven parameter recommendation in deep learning.

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).

Multiple timescale systems have long been a subject of extensive study, with geometric singular perturbation theory (GSPT) emerging as a common tool for analyzing such systems. In this work, we present a comprehensive study of ordinary differential equations in the form of boundary value problems that describe multiple timescale systems, focusing specifically on normally hyperbolic systems. We introduce a novel method, geometric singular perturbation-informed neural networks (GSPINNs), which combines the analytical rigor of GSPT with the modeling power of physics-informed neural networks. Our approach converts the system into a connecting problem, allowing for the discovery of detailed dynamical characteristics that provide deeper insights into the system's behavior. These solutions are then numerically approximated using GSPINNs. We validated our method, GSPINNs, through various challenging problems where traditional methods fail to capture the intricate dynamics of the system. For moderately nonhyperbolic, multiscale problems that are not extremely stiff, GSPINN remains stable enough to yield accurate solutions without resorting to blowup techniques, demonstrating its robustness in such cases. Our analysis and numerical experiments show that GSPINNs produce accurate and stable solutions for stiff fast-slow boundary value problems across a range of challenging examples, whereas conventional finite difference, shooting, and baseline PINN solvers often struggle. This work opens new opportunities for practical applications in modeling and simulating complex systems with varying timescales.

Adapting deep learning models to new domains often requires computationally intensive retraining and risks catastrophic forgetting. While fine-tuning enables domain-specific adaptation, it can reduce robustness to distribution shifts, impacting out-of-distribution (OOD) performance. Pre-trained zero-shot models like CLIP offer strong generalization but may suffer degraded robustness after fine-tuning. Building on Task Adaptive Parameter Sharing (TAPS), we propose a simple yet effective extension as a parameter-efficient fine-tuning (PEFT) method, using an indicator function to selectively activate Low-Rank Adaptation (LoRA) blocks. Our approach minimizes knowledge loss, retains its generalization strengths under domain shifts, and significantly reduces computational costs compared to traditional fine-tuning. We demonstrate that effective fine-tuning can be achieved with as few as 5% of active blocks, substantially improving efficiency. Evaluations on pre-trained models such as CLIP and DINO-ViT demonstrate our method's broad applicability and effectiveness in maintaining performance and knowledge retention.

Physics-Informed Neural Networks (PINNs) have gained widespread popularity for solving inverse and forward problems across a range of scientific and engineering domains. However, most existing PINN frameworks are limited to the Eulerian domain, where physical quantities are described at fixed spatial locations. In this work, we propose a novel PINN-based framework that couples Eulerian and Lagrangian perspectives by using particle trajectory data to reconstruct Eulerian velocity and pressure fields. We evaluate the performance of our method across three distinct fluid flow scenarios: two-dimensional external flow past a cylinder, two-dimensional internal flow in a confined geometry, and three-dimensional internal flow inside an airplane cabin. In all three cases, we successfully reconstruct the velocity field from Lagrangian particle data. Moreover, for the 2D external and internal flows, we recover the pressure field solely through the physics-informed learning process, without using any direct pressure measurements. We also conduct a sensitivity analysis to understand the effects of temporal resolution and particle count on the reconstruction accuracy. Our results show that smaller time-step sizes significantly improve the predictions, while the total number of particles has a comparatively smaller influence. These findings establish the potential of our coupled Eulerian-Lagrangian PINN framework as a powerful tool for enhancing experimental methods such as Particle Tracking Velocimetry (PTV). Looking ahead, this approach may be extended to infer hidden quantities such as pressure in three-dimensional flows or material properties like viscosity, opening new avenues for data-driven fluid dynamics in complex geometries.

This paper introduces MixDiff, a new self-supervised learning (SSL) pre-training framework that combines real and synthetic images. Unlike traditional SSL methods that predominantly use real images, MixDiff uses a variant of Stable Diffusion to replace an augmented instance of a real image, facilitating the learning of cross real-synthetic image representations. Our key insight is that while models trained solely on synthetic images underperform, combining real and synthetic data leads to more robust and adaptable representations. Experiments show MixDiff enhances SimCLR, BarlowTwins, and DINO across various robustness datasets and domain transfer tasks, boosting SimCLR's ImageNet-1K accuracy by 4.56%. Our framework also demonstrates comparable performance without needing any augmentations, a surprising finding in SSL where augmentations are typically crucial. Furthermore, MixDiff achieves similar results to SimCLR while requiring less real data, highlighting its efficiency in representation learning(1).

Reinforcement Learning from Human Feedback (RLHF) is increasingly used to align large language models (LLMs) with human preferences. However, the effectiveness of RLHF in addressing underlying biases remains unclear. This study investigates the relationship between RLHF and both covert and overt biases in LLMs, particularly focusing on biases against African Americans. We applied various RLHF techniques (DPO, ORPO, and RLOO) to Llama 3 8B and evaluated the covert and overt biases of the resulting models using matched-guise probing and explicit bias testing. We performed additional tests with DPO on different base models and datasets; among several implications, we found that SFT before RLHF calcifies model biases. Additionally, we extend the tools for measuring biases to multi-modal models. Through our experiments we collect evidence that indicates that current alignment techniques are inadequate for nebulous tasks such as mitigating covert biases, highlighting the need for capable datasets, data curating techniques, or alignment tools.

The Log-Periodic Power Law Singularity (LPPLS) model offers a general framework for capturing dynamics and predicting transition points in diverse natural and social systems. In this work, we present two calibration techniques for the LPPLS model using deep learning. First, we introduce the Mono-LPPLS-NN (M-LNN) model; for any given empirical time series, a unique M-LNN model is trained and shown to outperform state-of-the-art techniques in estimating the nonlinear parameters (tc; m; !) of the LPPLS model as evidenced by the comprehensive distribution of parameter errors. Second, we extend the M-LNN model to a more general model architecture, the Poly-LPPLS-NN (P-LNN), which is able to quickly estimate the nonlinear parameters of the LPPLS model for any given time-series of a fixed length, including previously unseen time-series during training. The Poly class of models train on many synthetic LPPLS time-series augmented with various noise structures in a supervised manner. Given enough training examples, the P-LNN models also outperform state-of-the-art techniques for estimating the parameters of the LPPLS model as evidenced by the comprehensive distribution of parameter errors. Additionally, this class of models is shown to substantially reduce the time to obtain parameter estimates. Finally, we present applications to the diagnostic and prediction of two financial bubble peaks (followed by their crash) and of a famous rockslide. These contributions provide a bridge between deep learning and the study of the prediction of transition times in complex time series.

Artificial neural networks often suffer from catastrophic forgetting, where learning new concepts leads to a complete loss of previously acquired knowledge. We observe that this issue is particularly magnified in vision transformers (ViTs), where post-pre-training and fine-tuning on new tasks can significantly degrade the model’s original general abilities. For instance, a DINO ViT-Base/16 pre-trained on ImageNet-1k loses over 70% accuracy on ImageNet-1k after just 10 iterations of fine-tuning on CIFAR-100. Overcoming this stability-plasticity dilemma is crucial for enabling ViTs to continuously learn and adapt to new domains while preserving their initial knowledge. In this work, we study two new parameter-efficient fine-tuning strategies: (1) Block Expansion, and (2) Low-rank adaptation (LoRA). Our experiments reveal that using either Block Expansion or LoRA on self-supervised pre-trained ViTs surpass fully fine-tuned ViTs in new domains while offering significantly greater parameter efficiency. Notably, we find that Block Expansion experiences only a minimal performance drop in the pre-training domain, thereby effectively mitigating catastrophic forgetting in pre-trained ViTs 1 .

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).

Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations in a forward and inverse manner using deep neural networks. However, training these networks can be challenging for multiscale problems. While statistical methods can be employed to scale the regression loss on data, it is generally challenging to scale the loss terms for equations. This paper proposes a method for scaling the mean squared loss terms in the objective function used to train PINNs. Instead of using automatic differentiation to calculate the temporal derivative, we use backward Euler discretization. This provides us with a scaling term for the equations. In this work, we consider the two and three-dimensional Navier-Stokes equations and determine the kinematic viscosity using the spatio-temporal data on the velocity and pressure fields. We first consider numerical datasets to test our method. We test the sensitivity of our method to the time step size, the number of timesteps, noise in the data, and spatial resolution. Finally, we use the velocity field obtained using Particle Image Velocimetry (PIV) experiments to generate a reference pressure field. We then test our framework using the velocity and reference pressure field.

Viscoelastic fluids are a class of fluids that exhibit both viscous and elastic nature. Modelling such fluids requires constitutive equations for the stress, and choosing the most appropriate constitutive relationship can be difficult. We present viscoelasticNet, a physics-informed deep learning framework that uses the velocity flow field to select the constitutive model and learn the stress field. Our framework requires data only for the velocity field, initial & boundary conditions for the stress tensor, and the boundary condition for the pressure field. Using this information, we learn the model parameters, the pressure field, and the stress tensor. This work considers three commonly used non-linear viscoelastic models: Oldroyd-B, Giesekus, and linear PTT. We demonstrate that our framework works well with noisy and sparse data. Our framework can be combined with velocity fields acquired from experimental techniques like particle image velocimetry to get the pressure & stress fields and model parameters for the constitutive equation. Once the model has been discovered using viscoelasticNet, the fluid can be simulated and modeled for further applications.

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in particular, play a central role in this hybridization. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multi-physics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multi-physics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers are presented. This critical review provides researchers and engineers with a solid starting point to comprehend how to integrate different layers of physics into neural networks.