Thermodynamic Properties Prediction via Machine Learning

# Thermodynamic Properties Prediction via Machine Learning

## Introduction & Motivation

Accurate prediction of thermodynamic properties (enthalpy, entropy, free energy) is critical for materials discovery and process design. ML models trained on computational or experimental data enable rapid screening and property estimation for novel compounds without expensive calculations.

Motivation: Predict thermodynamic properties for rapid materials discovery.

Applications: Property prediction, material screening, reaction feasibility, phase stability.

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## Core Concepts & Theory

### State Functions

Entropy, enthalpy, Gibbs free energy.

### Phase Diagrams

Stability regions and transitions.

### Reaction Spontaneity

ΔG and equilibrium prediction.

### Temperature Dependence

Heat capacity and temperature effects.

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## Mathematical Formulation

Gibbs Free Energy:
$$\Delta G = \Delta H - T\Delta S$$

Clausius-Clapeyron:
$$\ln \frac{P_2}{P_1} = -\frac{\Delta H}{R} \left(\frac{1}{T_2} - \frac{1}{T_1} ight)$$

Heat Capacity:
$$C_p = \left(\frac{\partial H}{\partial T} ight)_p$$

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## Advanced Theory & Extensions

### Equation of State

PVT relationships.

### Critical Phenomena

Near-critical behavior.

### Solution Thermodynamics

Mixing and activity coefficients.

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## Computational Considerations

Property Database: O(N·D) for N substances.

Model Training: O(N·D²) complexity.

Prediction: O(D) per compound.

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## Practical Implementation Strategies

### Feature Engineering

Molecular weight, SMILES descriptors.

### Temperature Scaling

Normalized temperature effects.

### Uncertainty Estimation

Prediction confidence intervals.

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## Benchmark Datasets & Evaluation

NIST Chemistry WebBook: Experimental data.

Materials Project: Computed properties.

Reaxys: Chemical database.

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## Key Challenges & Limitations

### Data Scarcity

Limited measurements for new compounds.

### Extrapolation Risk

Temperature and composition ranges.

### Phase Transitions

Discontinuities in properties.

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## Hyperparameter Tuning

Feature scaling: Normalization or standardization.

Model depth: 2-4 layers for neural networks.

Regularization: 1e-4 to 1e-2.

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## Real-World Applications & Case Studies

Battery Materials: Electrolyte properties.

Refrigerants: Thermodynamic screening.

Polymers: Thermal transitions.

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## Integration with Other Methods

Thermodynamics ML + reaction prediction; + phase diagrams; + optimization.

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## Summary & Key Takeaways

ML accelerates thermodynamic property prediction.

Principles:
1. Features: Molecular descriptors.
2. Data: Experimental or computational sources.
3. Model: Regression for continuous properties.
4. Prediction: Rapid property estimation.
5. Application: Materials discovery and screening.

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## Appendix: Practical Labs

### Lab 1: Property Prediction Model

import numpy as np

class ThermodynamicPredictor:
 def __init__(self, n_features=10):
 self.weights = np.random.randn(n_features) * 0.1
 self.bias = 0.0
 
 def train(self, X, y, epochs=100):
 """Train linear model"""
 for _ in range(epochs):
 y_pred = X @ self.weights + self.bias
 error = y_pred - y
 
 self.weights -= 0.01 * X.T @ error / len(y)
 self.bias -= 0.01 * np.mean(error)
 
 def predict(self, X):
 """Predict properties"""
 return X @ self.weights + self.bias

predictor = ThermodynamicPredictor()

# Generate training data
X_train = np.random.randn(50, 10)
y_train = X_train[:, 0] * 100 + X_train[:, 1] * 50 + np.random.randn(50) * 5

predictor.train(X_train, y_train)

X_test = np.random.randn(5, 10)
predictions = predictor.predict(X_test)

print(f"✓ Property predictions: {predictions[:3]}")

### Lab 2: Temperature Dependence

import numpy as np

def clausius_clapeyron(T1, T2, dH, R=8.314):
 """Estimate pressure change with temperature"""
 log_P_ratio = -(dH / R) * (1/T2 - 1/T1)
 return np.exp(log_P_ratio)

# Test
T1 = 298 # K
T2 = 373 # K
dH = 40.7e3 # J/mol (water vaporization)

P_ratio = clausius_clapeyron(T1, T2, dH)
print(f"✓ Clausius-Clapeyron: P_ratio = {P_ratio:.2f}")

### Lab 3: Gibbs Energy Prediction

import numpy as np

def predict_gibbs_energy(H, S, T):
 """Predict ΔG = ΔH - T·ΔS"""
 return H - T * S

# Test over temperature range
temperatures = np.linspace(273, 373, 10)
H = 100e3 # J/mol
S = 200 # J/mol·K

delta_G = np.array([predict_gibbs_energy(H, S, T) for T in temperatures])

print(f"✓ Gibbs energy calculation:")
print(f" Spontaneous reaction at T > {H/S:.0f} K")

### Lab 4: Materials Screening

import numpy as np

class MaterialScreener:
 def __init__(self, n_properties=5):
 self.property_targets = np.array([100, 50, -20, 5, 0.1])
 
 def evaluate_material(self, predicted_properties):
 """Score material based on properties"""
 distances = np.abs(predicted_properties - self.property_targets)
 score = 1.0 / (1.0 + np.mean(distances))
 
 return score
 
 def screen_candidates(self, candidate_predictions):
 """Rank candidate materials"""
 scores = np.array([self.evaluate_material(cp) for cp in candidate_predictions])
 ranking = np.argsort(scores)[::-1]
 
 return ranking, scores

screener = MaterialScreener()

# Generate candidate properties
candidates = np.random.randn(20, 5) * 50 + np.array([100, 50, -20, 5, 0.1])
ranking, scores = screener.screen_candidates(candidates)

print(f"✓ Top 3 candidates: {ranking[:3]}")
print(f"✓ Scores: {scores[ranking[:3]]}")

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