There are lot of buzz words about the birth of Genesis near end of 2024. However, diving deep into it, you would realize the essence of it is it’s applying AI to solve complex high-dimensional physics problem that traditional numerical analysis fall short of.

The big breakthrough they claim to realize 43 million fast frame per second (FPS) revolutionize how we can simulate engine or robot movements.

To illustrate, Here’s an example comparing AI and traditional numerical analysis approaches in Python for solving a heat equation:

Traditional Numerical Analysis Approach, finite difference approximation: Using SciPy’s solve_bvp function for boundary value problems:

import numpy as np
from scipy.integrate import solve_bvp

def heat_equation(x, y):
    return np.vstack((y[1], -y[0]))

def boundary_conditions(ya, yb):
    return np.array([ya[0], yb[0] - 1])

x = np.linspace(0, 1, 5)
y = np.zeros((2, x.size))

sol = solve_bvp(heat_equation, boundary_conditions, x, y)

AI-based Approach: neural network to solve the same heat equation problem:

import numpy as np
import tensorflow as tf

def neural_network_model():
    model = tf.keras.Sequential([
        tf.keras.layers.Dense(20, activation='tanh', input_shape=(1,)),
        tf.keras.layers.Dense(20, activation='tanh'),
        tf.keras.layers.Dense(1)
    ])
    return model

model = neural_network_model()

def loss_function(x):
    with tf.GradientTape() as tape:
        tape.watch(x)
        y = model(x)
        dy_dx = tape.gradient(y, x)
    
    d2y_dx2 = tf.gradients(dy_dx, x)[0]
    
    return tf.reduce_mean(tf.square(d2y_dx2 + y))

optimizer = tf.keras.optimizers.Adam(learning_rate=0.01)

for _ in range(1000):
    x = tf.random.uniform((100, 1))
    optimizer.minimize(lambda: loss_function(x), var_list=model.trainable_variables)

Key Differences

1. Methodology: The traditional method directly solves the equation, while the AI approach learns to approximate the solution.
2. Flexibility: AI methods can adapt to complex, high-dimensional problems more easily1.
3. Computational Efficiency: For repeated solutions or large-scale problems, AI methods may be more efficient once trained.
4. Accuracy: Traditional methods often provide higher precision for well-defined problems, while AI methods excel in handling uncertainty and complex systems.