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the trajectory of a ball under gravity.\n\n## Problem Description\n\nThis project models the height of a ball over time, governed by the equation:\n\n$$h(t) = h_0 + v_0t - 0.5gt^2$$\n\nwhere:\n- $h_0$ = 1.0 (initial height)\n- $v_0$ = 10.0 (initial velocity)\n- $g$ = 9.8 (acceleration due to gravity)\n\n## Implementation\n\nThe PINN uses a simple feedforward neural network to learn the solution while respecting:\n\n1. **Physics constraints**: The ODE $\\frac{dh}{dt} = v_0 - gt$\n2. **Initial condition**: $h(0) = h_0$\n3. **Data fitting**: Limited noisy measurements\n\nThe loss function combines these constraints with tunable weights:\nL = λ_data * L_data + λ_ode * L_ode + λ_ic * L_ic\n## Features\n\n- Automatic differentiation for computing derivatives in the physics loss\n- Synthetic data generation with adjustable noise\n- Visualization of PINN predictions against exact solution\n- Adjustable hyperparameters for loss weighting\n\n## Results\n![Alt text](image.png)\n\n\n**The PINN demonstrates excellent performance throughout the entire trajectory:**\n\n- The blue PINN prediction line closely tracks the black exact solution\n\n- Strong agreement across all time points from t=0 to t=6\n\n- The model successfully learns the physics despite the presence of noisy data\n\n- Even in regions with sparse or noisy data points, the PINN maintains accuracy\n- The trained PINN successfully recovers the true physics-based trajectory even with limited and noisy data points, demonstrating how incorporating physics into neural networks enhances their predictive power and generalization capabilities.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdino65-dev%2Fpinn-physics-informed-nn-","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdino65-dev%2Fpinn-physics-informed-nn-","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdino65-dev%2Fpinn-physics-informed-nn-/lists"}