Ever since the launch of large language models such as ChatGPT, scientists, engineers and public are trying to find various ways to automate complicated computing tasks with natural language processing. Researchers from Brown University have proposed an interesting framework which enables to use natural language processing (NLP) to help with scientific computing tasks. They called the framework MyCrunchGPT, which is a chatbot that can assist you with scientific machine learning (SciML) problems.

SciML can be challenging and time-consuming, as it involves many steps such as pre-processing, problem formulation, code generation, post-processing and analysis. Moreover, SciML may not be accessible to everyone, especially those who are not familiar with coding or physics.

This is where MyCrunchGPT comes in. MyCrunchGPT is a chatbot that uses ChatGPT to communicate with the user and guide them through the SciML workflow. ChatGPT is based on GPT-3, which is one of the most advanced NLP models that can generate natural and coherent texts based on user prompts. CrunchGPT leverages ChatGPT to understand the user's queries, provide relevant information, generate code snippets, plot graphs, and produce summary reports.

To demonstrate the capabilities of CrunchGPT, the authors of the paper present two examples: (1) design and optimization of 2D NACA airfoils, and (2) solving prototype fluid mechanics problems using physics-informed neural networks (PINNs). In both cases, CrunchGPT can help the user with various tasks such as defining the problem, choosing the parameters, running the simulations, visualizing the results, and validating the accuracy. The user can interact with CrunchGPT using natural language or simple commands, and get instant feedback and guidance.

The authors also provide a web-based user interface for CrunchGPT, which allows the user to choose from different options and see the results in real time. The user can also request a comprehensive summary report that contains all the information and outputs generated by CrunchGPT. The authors claim that CrunchGPT can be a useful tool for researchers, engineers, students, and educators who want to use SciML for their problems.

CrunchGPT is an innovative and exciting framework that shows the potential of using NLP for scientific computing. By using ChatGPT as a conductor, CrunchGPT can orchestrate the entire SciML workflow and make it easier and more accessible for everyone. If you want to learn more about CrunchGPT, you can read the full paper 

CrunchGPT Feature Image

MyCrunchGPT - A ChatGPT Framework for scientific machine learning

Have you ever wondered how to solve complex equations that describe how things change over time and space? These equations are called partial differential equations (PDEs) and they appear in many engineering problems, such as modeling fluid flow, heat transfer, wave propagation, or chemical reactions. Solving PDEs can be very challenging, especially when the domain is irregular or the equation is nonlinear.

A new machine learning technique called Laplace Neural Operator (LNO) can help solve PDEs more efficiently and accurately than traditional methods. LNO is a type of neural network that learns to map the input parameters of a PDE to its solution, without requiring any meshing or discretization of the domain. LNO uses the Laplace transform to decompose the input space into frequency components, which makes it suitable for problems with non-periodic signals or transient responses.

In a paper "LNO: Laplace Neural Operator for Solving Differential Equations", researchers from Brown University and MIT demonstrated the superior performance of LNO over another neural network technique called Fourier Neural Operator (FNO) in solving various PDEs. FNO uses the Fourier transform to decompose the input space, but it has limitations when dealing with non-periodic signals or undamped scenarios. LNO, on the other hand, can handle these cases better and exhibit exponential convergence.

The researchers tested LNO on three ordinary differential equations (ODEs) and three PDEs that have applications in physics and engineering. For example, one of the ODEs is the Duffing oscillator, which models a nonlinear spring-mass system that can exhibit chaotic behavior. One of the PDEs is the Euler-Bernoulli beam equation, which describes the deflection of a beam under load. The results showed that LNO can approximate the solutions of these equations more accurately than FNO, especially in capturing transient responses or complex boundary conditions.

LNO is not only a powerful tool for solving PDEs, but also a more interpretable and generalizable one. LNO incorporates the pole-residue relationship between the input and output spaces, which means that it can learn the natural frequencies and modes of the system. This can help engineers understand the underlying physics and phenomena better. Moreover, LNO can generalize to unseen inputs or domains better than FNO, which means that it can solve new problems with less data.

LNO is an exciting and promising direction for machine learning and engineering research. It shows how neural networks can help solve hard engineering problems that have been traditionally tackled by numerical methods. By applying LNO to real-world problems, engineers can achieve faster, more accurate, and more reliable solutions, while also gaining insights into the underlying physics and phenomena.

If you are interested in learning more about LNO and how it works, you can read the full paper 

. At DimensionLab, we are working on implementation of LNO into 

laplace-neural-operator

Laplace Neural Operator

Imagine a world where the design of wind turbines, the aerodynamics of vehicles, the optimization of electronics, the efficient conversion and storage of hydrogen fuel, and the exploration of alternative energy sources took merely a fraction of the time it currently does. Traditionally, these tasks have relied heavily on the creation of mathematical models - a painstakingly meticulous process carried out by human experts - followed by rigorous validation through numerical simulations. This age-old approach, while robust, is increasingly facing its limitations in a rapidly advancing world.

Enter the age of Artificial Intelligence, paving an unprecedented path in the realm of physics. From the seed of an incomplete problem description, AI has the ability to generate a mathematical model of extraordinary accuracy - a model so complex it could confound even the most brilliant of human minds. Our role, as humans, now pivots to becoming the validators of these AI-created models, rigorously testing and scrutinizing them from all perspectives to ensure their validity.

AI's disruptive presence extends further, offering a tremendous advantage when it comes to the utilization of these models in numerical simulations. The computational speed of these AI-generated models outpaces traditional methods by several thousand times, resulting in faster visualizations of physical phenomena for problem-solving, optimization, fault prediction, or technological advancement.

Embracing this accelerated process, we stand on the precipice of a research and development revolution. With the capacity to explore a vastly larger realm of possibilities in the same amount of time as before, we are pushing the boundaries of innovation and discovery. The future is here, and it is powered by AI.

It's essential to see how this revolutionary technology is applied in real-world scenarios. The exciting fusion of AI and physics isn't just theoretical; it's being leveraged right now, disrupting industries and accelerating progress. To truly appreciate the transformative power of AI in this field, let's delve into three compelling use-cases that exemplify this cutting-edge amalgamation at work.

Digital twin of Earth with fast weather prediction

An AI-driven approach was used to model global Earth weather leveraging 

work), which accurately forecasts high-resolution, fast-timescale variables such as the surface wind speed, precipitation, and atmospheric water vapor. It has important implications for planning wind energy resources, predicting extreme weather events such as tropical cyclones, extra-tropical cyclones, and atmospheric rivers.

, generating a week-long, accurate, 3-dimensional global weather prediction in under 10 seconds, reaching 

’s (IFS) state-of-the-art Numerical Weather Prediction (NWP) model, with 

 when dealing with model trained on meteorological dataset of global 30km vertical weather data. Once trained, however, FourCastNet 

 to generate a forecast than the IFS model. FourCastNet could be trained on currently available GPU hardware in about two months (~1,400 compute hours on a single A100 GPU) with available meteorological dataset from 40 years of global meteorological data collection (

Thanks to the speed of such a weather prediction model, it can be used in a wide variety of applications, such as energy and agricultural planning, transportation, and disaster mitigation. Here, we present few animations from visualizing the interactive simulation of FourCastNet model built with 

 framework and transformed into digital twin of Earth through 

In a world facing the dire realities of climate change, the quest for cleaner, greener energy is of paramount importance. 

, a leading name in renewable energy, has taken a giant leap in this direction, 

harnessing the power of physics-informed neural networks (PINNs)

 to revolutionize wind energy generation.

Before we delve into their breakthrough, it's important to understand the challenges of wind farm optimization. High-fidelity, transient simulation of a single wind turbine using traditional simulation software with LES turbulence modeling could take an astonishing 30-40 days. Now, consider a wind farm comprising tens, if not hundreds, of such turbines. Examining and reducing possible wake effects in real time, in tandem with fine-tuning wind farms to handle a multitude of wind and weather conditions, necessitates hundreds or even thousands of simulation runs and iterations. Traditionally, this was rendered infeasible due to the formidable time limitations and financial costs involved.

Enter the world of PINNs and AI-assisted positioning. Siemens Gamesa leveraged AI-based physics simulators trained using PINNs, leading to a dramatic acceleration in simulation times. Today, they can simulate tens of wind turbines in mere minutes, unlocking the power of inverse physics simulation for lightning-fast optimization of energy output.

But what does this breakthrough mean for our future? Imagine a world where efficient, green energy generation isn't just a distant ideal, but an everyday reality. The swift simulation and optimization process enabled by PINNs will allow us to rapidly set up and optimize wind farms, harnessing the untapped potential of wind energy at an unprecedented scale and speed.

This is more than just a technological triumph; it's a beacon of hope for a cleaner future. As we march forward, these advancements in AI and physics simulation will play a pivotal role in driving our transition towards sustainable, renewable energy sources.

Blood flow simulation in intracranial aneurysm

Computer simulation is highly beneficial for understanding the physics of blood flows within our bodies, particularly when dealing with dangerous health issues like aneurysms. Thanks to modern technology, we can create 3D geometries from the images of these anomalies using MRI and CT scans. However, such 3D representations vary for each patient, making it quite challenging to simulate blood flow and pressure for every unique case using traditional simulation software. It's a time-consuming process, but in these life-or-death situations, every minute counts. Quick understanding and decision-making can mean the difference between life and death.

With the help of physics-informed neural networks, doctors could analyze each anomaly in a few minutes instead of days or weeks. It’s like having a fast-forward button for crucial medical decisions. They can even explore multiple 'what if' scenarios in a single day, visualizing the potential outcomes of various treatments.

Armed with a comprehensive report of anticipated physiological factors, surgeons can better prepare for complex procedures and help avert disastrous medical events. In essence, these AI-powered tools will provide our medical professionals with a detailed roadmap for each unique patient journey, potentially saving more lives along the way.

PhysicsML

Harnessing AI: The New Frontier in Physics Simulation

We are happy to announce a launch of Siml.ai alpha release to the public!

 is a software platform for AI-based numerical simulation. It provides a visual editor for building high-performance physics simulators that leverage deep learning techniques (also called surrogate models). Additionally, the platform features tools for training these simulator models in powerful GPU-based cloud servers and easy-to-use AI inferencing and 3D visualization pipelines. There's a paradigm shift happening in the world of physics simulation. Deep learning methods are outperforming even the most optimized classical numerical solvers. The key components of these methods are 

 variations of Fourier neural operators (FNOs) and deep operator networks (DeepONets)

eliminate the need for meshing the geometries.

In complex numerical simulations, it’s important to precisely quantify the underlying physical mechanisms in order to analyze them. High-dimensional scientific simulations are computationally very expensive to run, and solvers and parameters must often be tuned individually to each system studied. 

Machine learning approaches tend to considerably decrease the load on computational resources by reducing the dimensionality of the studied problem and by factoring in the fact that 

AI-based simulators need to be trained only once

numerical simulation is computed during the inference of the model

. This, compared to computing physics every time a simulation is re-run, brings a large efficiency benefits together with shortened time for the actual computations as trained models.

Siml.ai platform provides a set of tools to easily create, train and deploy powerful physics-informed neural network models with complex physics and custom partial differential equations. Building an AI-based simulator is extremely easy in our Siml.ai Model Engineer.

Siml.ai Model Engineer is a tool for visually creating and optimizing general-purpose "learnable simulators" (e.g. for simulating fluid flows, multiphase flows, mechanical deformation, solid-fluid interaction and so on) using deep learning techniques. 

Our aim is to make the process of building such simulators simple, visual and understandable

Within the Siml.ai platform, Model Engineer has a powerful position of being a funnel through which we plan to build a large database of trained models by individual engineers, researchers or companies. This will allow us to create a new market for ready-to-use, "packaged" AI simulators – essentially a marketplace in which these entities can earn money from simulators trained by them by allowing other users to use them in their projects through 

Simulation Studio is a hybrid between web-based and native application for solving engineering and scientific problems leveraging pre-trained and optimized models of AI-based physics simulators. Since the simulations are computed by inferring these models, the time it takes to compute one timestep even of highly irregular simulation domain is in low tens of milliseconds, resulting in real-time simulation and visualization of physical phenomena. High-fidelity visualization rendering is achieved by leveraging the powerful Unreal Engine under the hood.

3D interface for high-fidelity, interactive in-situ visualizations

If you want see what is planned for the future, make sure to check out our 

We're also giving out 100% discount for 1 month for everybody who completes our 

 - you can get more information in our community Discord, which you can join 

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