AI Teams Unlock the Next Level of Scientific Discovery

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Author: Denis Avetisyan

A new agentic framework combines physics-informed machine learning with adaptive sampling to automate complex scientific computing tasks.

ATHENA establishes a hierarchical, agentic framework where large language models collaborate across conceptualization, policy formulation, implementation, and execution phases-a cycle driven by iterative code refinement and transparent access to planned actions, system states, and observational outputs-to achieve an evolutionary loop of autonomous scientific inquiry.
ATHENA establishes a hierarchical, agentic framework where large language models collaborate across conceptualization, policy formulation, implementation, and execution phases-a cycle driven by iterative code refinement and transparent access to planned actions, system states, and observational outputs-to achieve an evolutionary loop of autonomous scientific inquiry.

ATHENA leverages agentic systems, neural operators, and physics-informed learning to advance computational discovery.

Bridging the gap between theoretical scientific modeling and robust computational implementation remains a persistent challenge. This paper introduces ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms, an agentic framework designed to autonomously navigate the entire scientific research lifecycle. By framing computational exploration as a knowledge-driven diagnostic process, ATHENA achieves super-human performance in both identifying exact analytical solutions and deriving stable numerical solvers-surpassing limitations of current AI approaches. Could this paradigm shift, focusing on methodological innovation rather than mere automation, fundamentally accelerate the pace of scientific discovery?

Deconstructing the Fluid: The Limits of Traditional Modeling

Conventional computational fluid dynamics (CFD) tackles the intricacies of fluid motion by transforming the governing $Navier-Stokes$ equations-a set of partial differential equations describing fluid flow-into a discrete form suitable for numerical solution. This discretization process, while enabling practical simulations, inherently demands substantial computational resources. The complexity arises because accurately representing continuous fluid behavior requires a finely-grained mesh – a network of discrete points – throughout the simulated domain. As the desired accuracy increases, or the complexity of the flow (like turbulence) intensifies, the number of discrete elements grows exponentially, leading to a corresponding surge in memory requirements and processing time. Consequently, even with powerful supercomputers, simulating many real-world fluid dynamics problems remains a significant computational hurdle, prompting ongoing research into more efficient and scalable methods.

Simulating turbulent flows and intricate geometries remains a central hurdle in fluid dynamics, largely due to the chaotic nature of turbulence and the computational demands of resolving its myriad scales. The $Navier-Stokes$ equations, while theoretically capable of describing fluid motion, become extraordinarily difficult to solve numerically when confronted with such complexity. Further compounding the issue is the scarcity of reliable experimental data for validation; acquiring “ground truth” measurements within turbulent flows or around complex shapes is often prohibitively expensive, time-consuming, or even physically impossible. This lack of validation data introduces uncertainty into model development and hinders the ability to confidently predict fluid behavior in real-world applications, necessitating ongoing research into both advanced modeling techniques and innovative experimental approaches.

The pursuit of faster and more efficient fluid flow simulations is driven by the sheer breadth of real-world applications demanding accurate predictions. From forecasting atmospheric conditions – where even minor inaccuracies can lead to significant errors in weather prediction – to optimizing the aerodynamic performance of aircraft and vehicles, the computational cost of traditional methods often proves prohibitive. Industries like biomedical engineering, requiring precise modeling of blood flow, and chemical engineering, focused on optimizing reactor designs, similarly benefit from accelerated simulations. This demand extends to environmental modeling, such as predicting pollutant dispersion or the impact of climate change on ocean currents. Consequently, researchers are actively exploring innovative approaches – including machine learning techniques and reduced-order models – to achieve the necessary computational speed without sacrificing the fidelity of the $ Navier-Stokes $ equations and their ability to capture complex fluid behaviors.

Despite initial stochasticity introduced by noisy training data, a hybrid AI-numerical workflow successfully recovers a smooth and accurate velocity field with low errors (1.05% and 1.62%) by leveraging an inferred Reynolds number to refine a physics-based simulation.
Despite initial stochasticity introduced by noisy training data, a hybrid AI-numerical workflow successfully recovers a smooth and accurate velocity field with low errors (1.05% and 1.62%) by leveraging an inferred Reynolds number to refine a physics-based simulation.

Bridging the Gap: Imposing Order on Chaos with Physics-Informed AI

Physics-Informed Machine Learning (PIML) represents a significant departure from traditional machine learning approaches by explicitly incorporating underlying physical laws and constraints into model training. Unlike standard data-driven methods which rely solely on observed data, PIML leverages established physical principles, expressed as differential equations, boundary conditions, and conservation laws, as regularization terms within the loss function. This integration allows models to generalize more effectively with limited data, extrapolate beyond the training domain, and produce physically plausible solutions. The constraints are typically implemented as penalty terms, minimizing the discrepancy between the model’s predictions and the expected behavior dictated by the governing physics, thereby enhancing both accuracy and robustness. This approach is particularly beneficial in scenarios where data is scarce, noisy, or incomplete, and where adherence to physical principles is critical, such as in fluid dynamics, heat transfer, and structural mechanics.

Physics-Informed Neural Networks (PINNs) represent a class of neural networks trained to solve supervised learning tasks while respecting any given laws of physics described by partial differential equations. The core principle involves minimizing a loss function comprised of two components: a traditional mean squared error loss for data fitting and a physics loss representing the residual of the governing equation. This physics loss is calculated by substituting the neural network’s output – representing the solution to the physical problem – into the equation and evaluating the resulting error. Mathematically, the total loss is often expressed as $L = L_{data} + \lambda L_{physics}$, where $\lambda$ is a weighting factor balancing the contribution of data and physics. By minimizing this combined loss, PINNs effectively enforce adherence to known physical laws, leading to more accurate and physically plausible solutions even with limited training data.

Operator learning techniques, exemplified by DeepONet, represent a departure from traditional numerical methods for solving partial differential equations (PDEs). Instead of discretizing the domain and approximating solutions at discrete points, these methods directly learn the mapping between functions of space or time and the solution of the PDE. DeepONet, specifically, employs a deep neural network to approximate the operator $A$ in an equation of the form $u = Au$, where $u$ is the solution and $A$ is an operator. This approach offers potential efficiency gains as the learned operator can generalize to unseen data and higher resolutions without retraining, unlike discretization methods which require increased computational cost for finer grids. By learning the operator itself, the dimensionality of the problem is effectively reduced, allowing for more efficient representation and prediction of physical phenomena.

Switching from a Fourier to a Periodic Wavelet basis, as guided by human input, enabled the system to accurately resolve a discontinuous solution with minimal oscillations.
Switching from a Fourier to a Periodic Wavelet basis, as guided by human input, enabled the system to accurately resolve a discontinuous solution with minimal oscillations.

Sharpening the Tools: Data-Driven Refinement of Simulations

Adaptive Sampling is a technique used to optimize machine learning model training by prioritizing data points that yield the greatest improvement in model accuracy. Instead of randomly selecting training data, this method iteratively identifies regions of the input space where the model exhibits the highest error or uncertainty. By concentrating training efforts on these problematic areas, Adaptive Sampling achieves comparable or superior accuracy to traditional methods while requiring a significantly smaller training dataset. This efficiency stems from the targeted approach, which avoids redundant training on data the model already predicts well and focuses resources where they are most impactful, ultimately reducing computational cost and training time.

Artificial Intelligence Velocimetry (AIV) addresses limitations in fluid dynamics data acquisition by integrating machine learning with numerical simulation. Traditional methods require dense sensor networks or computationally expensive simulations to fully characterize flow fields; AIV circumvents this by leveraging trained models to infer velocity fields from sparse data. This is achieved by using numerical simulations to generate training data, which is then used to train a machine learning model to predict the complete flow field given limited observational data. The technique effectively reconstructs flow information, reducing the need for extensive data collection and enabling analysis in scenarios where comprehensive measurement is impractical or impossible.

Evaluation of the combined adaptive sampling and AI velocimetry techniques was performed using the Lid-Driven Cavity benchmark problem. Results indicate a high degree of accuracy in predicting complex flow patterns; specifically, the relative L2 error for the u-velocity component was measured at 1.05%, while the relative L2 error for the v-velocity component was 1.62%. These error rates demonstrate the effectiveness of the methodology in accurately reconstructing flow fields from limited data, as validated by comparison to established solutions for this standard fluid dynamics problem.

The Advisor Agent demonstrates advanced problem-solving capabilities by successfully validating complex simulations-including Helmholtz and Korteweg-de Vries equations-through manufactured solutions, symbolic reasoning, and rigorous boundary condition enforcement, all confirmed by stable convergence and high-fidelity results.
The Advisor Agent demonstrates advanced problem-solving capabilities by successfully validating complex simulations-including Helmholtz and Korteweg-de Vries equations-through manufactured solutions, symbolic reasoning, and rigorous boundary condition enforcement, all confirmed by stable convergence and high-fidelity results.

Unlocking the Unsolvable: Reverse Engineering Reality with AI

The confluence of Artificial Intelligence Velocimetry and Physics-Informed Machine Learning is redefining the landscape of inverse problems, traditionally considered unsolvable due to their ill-posed nature. This innovative approach leverages AI to meticulously map velocity fields, effectively creating a detailed observational dataset. Simultaneously, the framework integrates fundamental physics – governing equations like the Navier-Stokes equations – directly into the machine learning process. This integration isn’t merely about applying AI; it’s about constraining the AI’s learning with established physical laws, ensuring solutions are not only accurate but also physically plausible. The result is a powerful system capable of inferring hidden parameters or initial conditions from limited observational data, unlocking insights in complex systems where direct measurement is impossible or impractical. Consequently, fields reliant on reverse engineering solutions – such as fluid dynamics and materials science – are poised to benefit from unprecedented analytical capabilities.

The ability to solve previously intractable inverse problems through AI Velocimetry and Physics-Informed Machine Learning extends far beyond theoretical advancement, promising substantial progress in several critical engineering domains. Flow control systems, for instance, stand to benefit from real-time analysis and adjustments, optimizing fluid dynamics for reduced drag and increased efficiency. Similarly, turbulence modeling, a notoriously complex field, gains a powerful new tool for accurate prediction and simulation of chaotic flow regimes. Perhaps most visibly, the design of aerodynamic surfaces – from aircraft wings to wind turbine blades – can be revolutionized, allowing engineers to explore and implement designs that maximize lift, minimize resistance, and ultimately enhance performance. This computational leap enables the creation of more efficient vehicles, reduces energy consumption, and fosters innovation across diverse sectors reliant on fluid dynamics.

Demonstrating a remarkable level of accuracy, the developed framework successfully solved the viscous Burgers equation with a Mean Squared Error (MSE) of just $4.76e-14$. This performance extends beyond mere equation solving, as the system accurately inferred the Reynolds Number – a crucial parameter in fluid dynamics – estimating a value of 525. This inferred value closely aligns with the true Reynolds Number of 500, highlighting the framework’s capacity for not only reconstructing solutions but also reliably determining underlying physical properties. Such precision suggests the potential for highly detailed and trustworthy analysis in complex fluid flow scenarios, paving the way for advancements in areas like turbulence modeling and aerodynamic design.

The convergence of AI Velocimetry and Physics-Informed Machine Learning establishes a pathway toward instantaneous flow field analysis and subsequent optimization of engineering designs. This capability transcends traditional computational fluid dynamics, enabling real-time adjustments to systems for maximized efficiency and performance. Applications span diverse fields, from refining the aerodynamic profiles of aircraft and vehicles – reducing drag and enhancing fuel economy – to optimizing the internal flows within pumps and turbines for increased power output. Furthermore, the technology promises breakthroughs in turbulence modeling, allowing for more accurate predictions and control of chaotic fluid behavior, ultimately leading to more robust and reliable engineering systems across multiple industries. The potential extends to flow control mechanisms, where dynamic adjustments can mitigate unwanted effects and enhance desired outcomes in complex fluidic environments.

ATHENA stabilized a compressible Rayleigh-Taylor instability simulation by autonomously adapting the mesh to the domain’s aspect ratio and enforcing hydrostatic pressure, preventing spurious waves and enabling stable, complex mixing.
ATHENA stabilized a compressible Rayleigh-Taylor instability simulation by autonomously adapting the mesh to the domain’s aspect ratio and enforcing hydrostatic pressure, preventing spurious waves and enabling stable, complex mixing.

ATHENA, as detailed in the study, embodies a systematic dismantling of traditional scientific computing methods. The framework doesn’t simply apply algorithms; it actively probes their boundaries through agentic exploration and hierarchical evolution. This mirrors a core tenet of understanding any complex system-taking it apart to see how it ticks. As Brian Kernighan aptly stated, “Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it.” ATHENA’s adaptive sampling and physics-informed learning aren’t about crafting perfect solutions upfront; they’re about intelligently breaking down problems and iteratively refining the approach, acknowledging the inherent complexity and the necessity of ‘debugging’ the very models themselves. The system essentially reverses engineers the path to discovery.

Where Do We Go From Here?

ATHENA, as presented, doesn’t so much solve scientific discovery as relocate the points of failure. The framework elegantly shifts the burden from explicit algorithm design to the curation of agentic behavior and reward structures. This is a useful, if subtle, distinction. It acknowledges that complete automation-a self-improving system free of human intervention-remains a stubbornly elusive goal. The true limitation isn’t the neural network’s capacity, but the inherent ambiguity of defining ‘correct’ in complex systems. A perfectly accurate simulation of a chaotic process, after all, is indistinguishable from noise – the universe, it seems, prefers obfuscation.

Future work will inevitably focus on refining the adaptive sampling methodologies. But a more interesting challenge lies in exploring the emergent properties of multi-agent systems. Can an ensemble of ATHENA-like agents, each pursuing slightly different reward functions, collectively navigate the solution space more efficiently than a single, monolithic framework? The potential for internal conflict – agents actively disproving each other’s hypotheses – should be viewed not as a bug, but as a feature. Rigor, one suspects, is born from adversarial testing, even within artificial intelligence.

Ultimately, ATHENA, and systems like it, are tools for accelerating the process of reverse-engineering reality. They are not replacements for intuition, skepticism, or the sheer stubbornness required to challenge established dogma. The most fruitful discoveries, one anticipates, will occur at the interface between automated computation and human curiosity-where the machine illuminates the possibilities, and the scientist decides which are worth pursuing.

Original article: https://arxiv.org/pdf/2512.03476.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-04 19:35