Computational Materials Science
Physically interpretable interatomic potentials via symbolic regression and reinforcement learning
This paper demonstrates a novel approach using symbolic regression (SR) with equation learner networks and reinforcement learning to derive interpretable equations for interatomic interactions. By training on extensive DFT data, the SR-derived models (SR1 and SR2) significantly outperform traditional fixed-form potentials like Sutton-Chen EAM in predicting key material properties, including lattice constants, cohesive energies, equations of state, elastic constants, phonon dispersion, defect formation energies, and phase transformation, with improved accuracy and transferability across diverse configurations.
Transforming Enterprise AI with Interpretability
Our groundbreaking Symbolic Regression (SR) approach, enhanced by Reinforcement Learning, delivers not just highly accurate predictive models for materials science but also provides fully interpretable physical equations. This eliminates the 'black box' problem of traditional machine learning, offering clear, actionable insights for enterprise applications in advanced materials design, manufacturing, and R&D. Enterprises can now deploy AI solutions with confidence, understanding the fundamental relationships governing their systems.
~87%
Reduction in Energy MAE vs. SC-EAM (SR1, Near-Ground)
~4.41 µs/atom/step
Execution Speed (SR2)
16%
C44 Elastic Constant Error (SR2 vs DFT)
~4.5%
Melting Point Deviation from Experiment (SR1/SR2)
Deep Analysis & Enterprise Applications
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Symbolic Regression (SR) models, SR1 and SR2, consistently outperform the traditional Sutton-Chen Embedded Atom Model (SC-EAM) across various material properties. This includes significantly improved accuracy in predicting Equations of State (EOS), phonon dispersion, defect formation energies, and surface/bulk energetics. The enhanced flexibility of SR models allows for robust predictions across a broad range of atomic configurations, from near-ground to far-from-equilibrium states.
87%
Reduction in Energy MAE vs. SC-EAM (SR1, Near-Ground)
Enterprise Process Flow
Generate DFT Data
→
EqNN Training (MCTS + GD)
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Derive SR Models (SR1/SR2)
→
Validate Properties
→
Deploy Interatomic Potential
| Property | DFT | SC-EAM | SR1 | SR2 | Exp. |
|---|---|---|---|---|---|
| C11 (GPa) | 180 | 170 | 166.94 | 186.21 | 176[57] |
| C12 (GPa) | 127 | 130 | 112.27 | 119.11 | 125[57] |
| C44 (GPa) | 79 | 58 | 64.84 | 66.40 | 82[57] |
| SFE (mJ/m²) | 41[58] | 32.45 | 49.84 | 66.40 | N/A |
| Evac (eV) | N/A | 0.875 | 1.32 | 1.37 | 1.29[59] |
| Eint (eV) | 2.902[60] | 2.72 | 3.08 | 3.02 | N/A |
Our SR models achieve near-classical EAM performance in terms of computational speed, while delivering accuracy comparable to DFT. This balance makes them computationally tractable for large-scale molecular dynamics simulations, offering a significant advantage over more expensive MLIPs that often require specialized hardware.
300+x
Faster than other MLIPs (e.g., GAP vs. SR2)
| Potential | Timing (µs/atom/step) |
|---|---|
| SR1 | 4.50 |
| SR2 | 4.41 |
| Sutton-Chen EAM | 3.60 |
| MLIPs (GAP) | 1512 [62] |
| MLIPs (SNAP) | 40.9 [62] |
| MLIPs (qSNAP) | 41.3 [62] |
| MLIPs (MTP) | 20.7 [62] |
| MLIPs (MACE-Small) | 42 [61] |
A key advantage of Symbolic Regression is the explicit, analytical form of the derived equations. Unlike "black-box" machine learning models, SR provides transparent insights into the underlying physical interactions, allowing researchers and engineers to understand the mechanisms governing material behavior and to derive actionable insights for design and optimization.
Unlocking Design Insights with Transparent AI
For material engineers, understanding why a potential predicts certain material behaviors is as crucial as the prediction itself. Our Symbolic Regression (SR) models provide explicit, mathematical equations for interatomic interactions, directly revealing underlying physical principles. This transparency enables engineers to gain deeper insights into material properties, optimize design parameters with confidence, and accelerate innovation, moving beyond trial-and-error to knowledge-driven development. This contrasts sharply with opaque "black-box" MLIPs, where predictions lack mechanistic explanations.
- Direct Physical Insight: Understand the exact mathematical forms governing material interactions.
- Accelerated Innovation: Use insights to guide new material development and process optimization.
- Enhanced Trust & Validation: Verify model predictions against established physical laws.
- Reduced R&D Cycles: Pinpoint key variables and accelerate experimental design.
Accurate prediction of thermodynamic properties, such as melting point, is a stringent test for interatomic potentials. Our SR models demonstrated high fidelity in capturing copper's melting dynamics and phase transitions, with a low deviation from experimental values, making them reliable for high-temperature applications.
4.5%
Deviation from Experimental Melting Point (SR1/SR2)
Reliable Simulations for High-Temperature Applications
Accurately predicting melting points is a critical test for any interatomic potential. Our SR models demonstrated a remarkable 4.5% deviation from the experimental melting point of copper, significantly outperforming traditional EAM models. This precision ensures that our potentials reliably capture the complex interplay of vibrational entropy, cohesive energy, and structural dynamics, which are essential for simulating materials in extreme conditions. For industries involved in additive manufacturing, high-temperature alloys, or nuclear materials, this means more trustworthy simulations and reduced risk in materials design and process optimization.
- Accurate Phase Transitions: Model melting and solidification with high fidelity.
- Enhanced Thermomechanical Fidelity: Reliable predictions for materials under heat.
- Reduced Simulation Artifacts: Avoid common issues like superheating or undercooling.
- Robust Design for Extreme Environments: Trustworthy data for critical applications.
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Your Journey to Interpretable AI
Our structured implementation roadmap ensures a seamless integration of symbolic regression and reinforcement learning into your enterprise workflows, maximizing value and minimizing disruption.
Phase 1: Discovery & Strategy
Collaborative workshops to identify key challenges, data sources, and desired outcomes. Define success metrics and a tailored AI strategy.
Phase 2: Data Engineering & Model Development
Prepare and cleanse your enterprise data, then develop custom symbolic regression models using our advanced EqNN and RL frameworks, focusing on interpretability and accuracy.
Phase 3: Integration & Validation
Seamlessly integrate developed AI models into your existing systems. Rigorous validation against real-world data and expert feedback to ensure robust performance.
Phase 4: Deployment & Optimization
Full-scale deployment of interpretable AI solutions. Continuous monitoring, performance optimization, and ongoing support to maximize long-term value.
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