Chris Hill

Rishikesh Ranade, Chris Hill, Lalit Ghule et al.

In this paper we show that our Machine Learning (ML) approach, CoMLSim (Composable Machine Learning Simulator), can simulate PDEs on highly-resolved grids with higher accuracy and generalization to out-of-distribution source terms and geometries than traditional ML baselines. Our unique approach combines key principles of traditional PDE solvers with local-learning and low-dimensional manifold techniques to iteratively simulate PDEs on large computational domains. The proposed approach is validated on more than 5 steady-state PDEs across different PDE conditions on highly-resolved grids and comparisons are made with the commercial solver, Ansys Fluent as well as 4 other state-of-the-art ML methods. The numerical experiments show that our approach outperforms ML baselines in terms of 1) accuracy across quantitative metrics and 2) generalization to out-of-distribution conditions as well as domain sizes. Additionally, we provide results for a large number of ablations experiments conducted to highlight components of our approach that strongly influence the results. We conclude that our local-learning and iterative-inferencing approach reduces the challenge of generalization that most ML models face.

Qidong Yang, Jonathan Giezendanner, Daniel Salles Civitarese et al.

Urgent applications like wildfire management and renewable energy generation require precise, localized weather forecasts near the Earth's surface. However, forecasts produced by machine learning models or numerical weather prediction systems are typically generated on large-scale regular grids, where direct downscaling fails to capture fine-grained, near-surface weather patterns. In this work, we propose a multi-modal transformer model trained end-to-end to downscale gridded forecasts to off-grid locations of interest. Our model directly combines local historical weather observations (e.g., wind, temperature, dewpoint) with gridded forecasts to produce locally accurate predictions at various lead times. Multiple data modalities are collected and concatenated at station-level locations, treated as a token at each station. Using self-attention, the token corresponding to the target location aggregates information from its neighboring tokens. Experiments using weather stations across the Northeastern United States show that our model outperforms a range of data-driven and non-data-driven off-grid forecasting methods. They also reveal that direct input of station data provides a phase shift in local weather forecasting accuracy, reducing the prediction error by up to 80% compared to pure gridded data based models. This approach demonstrates how to bridge the gap between large-scale weather models and locally accurate forecasts to support high-stakes, location-sensitive decision-making.

Rishikesh Ranade, Chris Hill, Haiyang He et al.

Numerical simulations for engineering applications solve partial differential equations (PDE) to model various physical processes. Traditional PDE solvers are very accurate but computationally costly. On the other hand, Machine Learning (ML) methods offer a significant computational speedup but face challenges with accuracy and generalization to different PDE conditions, such as geometry, boundary conditions, initial conditions and PDE source terms. In this work, we propose a novel ML-based approach, CoAE-MLSim (Composable AutoEncoder Machine Learning Simulation), which is an unsupervised, lower-dimensional, local method, that is motivated from key ideas used in commercial PDE solvers. This allows our approach to learn better with relatively fewer samples of PDE solutions. The proposed ML-approach is compared against commercial solvers for better benchmarks as well as latest ML-approaches for solving PDEs. It is tested for a variety of complex engineering cases to demonstrate its computational speed, accuracy, scalability, and generalization across different PDE conditions. The results show that our approach captures physics accurately across all metrics of comparison (including measures such as results on section cuts and lines).

Rishikesh Ranade, Chris Hill, Haiyang He et al.

In this work we propose a hybrid solver to solve partial differential equation (PDE)s in the latent space. The solver uses an iterative inferencing strategy combined with solution initialization to improve generalization of PDE solutions. The solver is tested on an engineering case and the results show that it can generalize well to several PDE conditions.

Jeffrey C. Carver, Ian A. Cosden, Chris Hill et al.

Research software is a class of software developed to support research. Today a wealth of such software is created daily in universities, government, and commercial research enterprises worldwide. The sustainability of this software faces particular challenges due, at least in part, to the type of people who develop it. These Research Software Engineers (RSEs) face challenges in developing and sustaining software that differ from those faced by the developers of traditional software. As a result, professional associations have begun to provide support, advocacy, and resources for RSEs. These benefits are critical to sustaining RSEs, especially in environments where their contributions are often undervalued and not rewarded. This paper focuses on how professional associations, such as the United States Research Software Engineer Association (US-RSE), can provide this.

Rishikesh Ranade, Chris Hill, Jay Pathak

Over the last few decades, existing Partial Differential Equation (PDE) solvers have demonstrated a tremendous success in solving complex, non-linear PDEs. Although accurate, these PDE solvers are computationally costly. With the advances in Machine Learning (ML) technologies, there has been a significant increase in the research of using ML to solve PDEs. The goal of this work is to develop an ML-based PDE solver, that couples important characteristics of existing PDE solvers with ML technologies. The two solver characteristics that have been adopted in this work are: 1) the use of discretization-based schemes to approximate spatio-temporal partial derivatives and 2) the use of iterative algorithms to solve linearized PDEs in their discrete form. In the presence of highly non-linear, coupled PDE solutions, these strategies can be very important in achieving good accuracy, better stability and faster convergence. Our ML-solver, DiscretizationNet, employs a generative CNN-based encoder-decoder model with PDE variables as both input and output features. During training, the discretization schemes are implemented inside the computational graph to enable faster GPU computation of PDE residuals, which are used to update network weights that result into converged solutions. A novel iterative capability is implemented during the network training to improve the stability and convergence of the ML-solver. The ML-Solver is demonstrated to solve the steady, incompressible Navier-Stokes equations in 3-D for several cases such as, lid-driven cavity, flow past a cylinder and conjugate heat transfer.