Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higherorder optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradientdescent-based learning pipeline, replacing the regular gradient of the physical process. We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. Wefind that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higherorder optimization methods with machine learning techniques.

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions.We propose a novel hybrid training approach that combines higher-order optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradient-descent-based learning pipeline, replacing the regular gradient of the physical process.We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.

With rapid urbanization, predicting urban microclimates has become critical, as it affects building energy demand and public health risks. However, existing generative and homogeneous graph approaches fall short in capturing physical consistency, spatial dependencies, and temporal variability. To address this, we introduce UrbanGraph, a physics-informed framework integrating heterogeneous and dynamic spatio-temporal graphs. It encodes key physical processes -- vegetation evapotranspiration, shading, and convective diffusion -- while modeling complex spatial dependencies among diverse urban entities and their temporal evolution. We evaluate UrbanGraph on UMC4/12, a physics-based simulation dataset covering diverse urban configurations and climates. Results show that UrbanGraph improves $R^2$ by up to 10.8% and reduces FLOPs by 17.0% over all baselines, with heterogeneous and dynamic graphs contributing 3.5% and 7.1% gains. Our dataset provides the first high-resolution benchmark for spatio-temporal microclimate modeling, and our method extends to broader urban heterogeneous dynamic computing tasks.

Industrial Control Systems (ICS) manage critical infrastructures like power grids and water treatment plants. Cyberattacks on ICSs can disrupt operations, causing severe economic, environmental, and safety issues. For example, undetected pollution in a water plant can put the lives of thousands at stake. ICS researchers have increasingly turned to honeypots -- decoy systems designed to attract attackers, study their behaviors, and eventually improve defensive mechanisms. However, existing ICS honeypots struggle to replicate the ICS physical process, making them susceptible to detection. Accurately simulating the noise in ICS physical processes is challenging because different factors produce it, including sensor imperfections and external interferences. In this paper, we propose SimProcess, a novel framework to rank the fidelity of ICS simulations by evaluating how closely they resemble real-world and noisy physical processes. It measures the simulation distance from a target system by estimating the noise distribution with machine learning models like Random Forest. Unlike existing solutions that require detailed mathematical models or are limited to simple systems, SimProcess operates with only a timeseries of measurements from the real system, making it applicable to a broader range of complex dynamic systems. We demonstrate the framework's effectiveness through a case study using real-world power grid data from the EPIC testbed. We compare the performance of various simulation methods, including static and generative noise techniques. Our model correctly classifies real samples with a recall of up to 1.0. It also identifies Gaussian and Gaussian Mixture as the best distribution to simulate our power systems, together with a generative solution provided by an autoencoder, thereby helping developers to improve honeypot fidelity. Additionally, we make our code publicly available.

Similar to conventional video generation, current deep learning-based weather prediction frameworks often lack explicit physical constraints, leading to unphysical outputs that limit their reliability for operational forecasting. Among various physical processes requiring proper representation, radiation plays a fundamental role as it drives Earth's weather and climate systems. However, accurate simulation of radiative transfer processes remains challenging for traditional numerical weather prediction (NWP) models due to their inherent complexity and high computational costs. Here, we propose FuXi-RTM, a hybrid physics-guided deep learning framework designed to enhance weather forecast accuracy while enforcing physical consistency. FuXi-RTM integrates a primary forecasting model (FuXi) with a fixed deep learning-based radiative transfer model (DLRTM) surrogate that efficiently replaces conventional radiation parameterization schemes. This represents the first deep learning-based weather forecasting framework to explicitly incorporate physical process modeling. Evaluated over a comprehensive 5-year dataset, FuXi-RTM outperforms its unconstrained counterpart in 88.51% of 3320 variable and lead time combinations, with improvements in radiative flux predictions. By incorporating additional physical processes, FuXi-RTM paves the way for next-generation weather forecasting systems that are both accurate and physically consistent.

Physical simulations are essential tools across critical fields such as mechanical and aerospace engineering, chemistry, meteorology, etc.. While neural operators, particularly the Fourier Neural Operator (FNO), have shown promise in predicting simulation results with impressive performance and efficiency, they face limitations when handling real-world scenarios involving coupled multiphysics outputs. Current neural operator methods either overlook the correlations between multiple physical processes or employ simplistic architectures that inadequately capture these relationships. To overcome these challenges, we introduce a novel coupled multi-physics neural operator learning (COMPOL) framework that extends the capabilities of Fourier operator layers to model interactions among multiple physical processes. Our approach implements feature aggregation through recurrent and attention mechanisms, enabling comprehensive modeling of coupled interactions. Our method's core is an innovative system for aggregating latent features from multi-physics processes. These aggregated features serve as enriched information sources for neural operator layers, allowing our framework to capture complex physical relationships accurately. We evaluated our coupled multi-physics neural operator across diverse physical simulation tasks, including biological systems, fluid mechanics, and multiphase flow in porous media. Our proposed model demonstrates a two to three-fold improvement in predictive performance compared to existing approaches.

One of the major sources of uncertainty in the current generation of Global Climate Models (GCMs) is the representation of sub-grid scale physical processes. Over the years, a series of deep-learning-based parameterization schemes have been developed and tested on both idealized and real-geography GCMs. However, datasets on which previous deep-learning models were trained either contain limited variables or have low spatial-temporal coverage, which can not fully simulate the parameterization process. Additionally, these schemes rely on classical architectures while the latest attention mechanism used in Transformer models remains unexplored in this field. In this paper, we propose Paraformer, a "memory-aware" Transformer-based model on ClimSim, the largest dataset ever created for climate parameterization. Our results demonstrate that the proposed model successfully captures the complex non-linear dependencies in the sub-grid scale variables and outperforms classical deep-learning architectures. This work highlights the applicability of the attenuation mechanism in this field and provides valuable insights for developing future deep-learning-based climate parameterization schemes.