Fix heat equation solution

app.py

@@ -6,10 +6,10 @@ import numpy as np
 import gradio as gr
 import plotly.graph_objs as go
 
-glob_a = -2
-glob_b = -2
-glob_c = -4
-glob_d = 7
+glob_k = 0.0025
+glob_a = -2.
+glob_b = 4.
+glob_c = 7.5
 
 
 def clear_npz():
@@ -26,12 +26,13 @@ def clear_npz():
                 print(f"Failed to delete {file_path}. Reason: {e}")
 
 
-def complex_heat_eq_solution(x, t, a=glob_a, b=glob_b, c=glob_c, d=glob_d, k=0.5):
-    global glob_a, glob_b, glob_c, glob_d
+def complex_heat_eq_solution(x, t, k=glob_k, a=glob_a, b=glob_b, c=glob_c):
+    global glob_k, glob_a, glob_b, glob_c
+    glob_k, glob_a, glob_b, glob_c = k, a, b, c
     return (
-        np.exp(-k * t) * np.sin(np.pi * x)
-        + 0.5 * np.exp(glob_a * k * t) * np.sin(glob_b * np.pi * x)
-        + 0.25 * np.exp(glob_c * k * t) * np.sin(glob_d * np.pi * x)
+        np.exp(-glob_k * (glob_b * np.pi) ** 2 * t) * np.cos(glob_a * np.pi * x)
+        + np.exp(-glob_k * (glob_b * np.pi) ** 2 * t) * np.sin(glob_b * np.pi * x)
+        + np.exp(-glob_k * (glob_c * np.pi) ** 2 * t) * np.sin(glob_c * np.pi * x)
     )
 
 
@@ -358,15 +359,15 @@ def train_coefficients(m, kernel):
     return f"Training completed in {time.time() - start_time:.2f} seconds. The average error is {avg_err}."
 
 
-def plot_function(a, b, c, d, k=0.5):
-    global glob_a, glob_b, glob_c, glob_d
+def plot_function(k, a, b, c):
+    global glob_k, glob_a, glob_b, glob_c
 
-    glob_a, glob_b, glob_c, glob_d = a, b, c, d
+    glob_k, glob_a, glob_b, glob_c = k, a, b, c
 
     x = np.linspace(0, 1, 100)
     t = np.linspace(0, 5, 500)
     X, T = np.meshgrid(x, t)  # Create the mesh grid
-    Z = complex_heat_eq_solution(X, T, a, b, c, d)
+    Z = complex_heat_eq_solution(X, T, glob_k, glob_a, glob_b, glob_c)
 
     traces = []
     traces.append(
@@ -419,19 +420,25 @@ def plot_function(a, b, c, d, k=0.5):
 
     return fig
 
+
 def plot_all(m, kernel):
     # Generate the plot content (replace this with your actual plot logic)
-    approx_fig = plot_heat_equation(m, kernel)  # Replace with your function for approx_plot
-    error_fig = plot_errors(m, kernel)    # Replace with your function for error_plot
-    
+    approx_fig = plot_heat_equation(
+        m, kernel
+    )  # Replace with your function for approx_plot
+    error_fig = plot_errors(m, kernel)  # Replace with your function for error_plot
+
     # Return the figures and make the plots visible
     return (
         gr.update(visible=True, value=approx_fig),
         gr.update(visible=True, value=error_fig),
     )
 
+
 # Gradio interface
 def create_gradio_ui():
+    global glob_k, glob_a, glob_b, glob_c
+    
     # Get the initial available files
     with gr.Blocks() as demo:
         gr.Markdown("# Learn the Coefficients for the Heat Equation using the RFM")
@@ -447,39 +454,39 @@ def create_gradio_ui():
 
         with gr.Row():
             with gr.Column():
+                k_slider = gr.Slider(
+                    minimum=0.0001, maximum=0.1, step=0.0001, value=glob_k, label="k"
+                )
                 a_slider = gr.Slider(
-                    minimum=-10, maximum=-1, step=1, value=-2, label="a"
+                    minimum=-10, maximum=10, step=0.1, value=glob_a, label="a"
                 )
                 b_slider = gr.Slider(
-                    minimum=-10, maximum=10, step=1, value=-2, label="b"
+                    minimum=-10, maximum=10, step=0.1, value=glob_b, label="b"
                 )
                 c_slider = gr.Slider(
-                    minimum=-10, maximum=-1, step=1, value=-4, label="c"
-                )
-                d_slider = gr.Slider(
-                    minimum=-10, maximum=10, step=1, value=7, label="d"
+                    minimum=-10, maximum=10, step=0.1, value=glob_c, label="c"
                 )
 
             plot_output = gr.Plot()
-
-        a_slider.change(
+            
+        k_slider.change(
             fn=plot_function,
-            inputs=[a_slider, b_slider, c_slider, d_slider],
+            inputs=[k_slider, a_slider, b_slider, c_slider],
             outputs=[plot_output],
         )
-        b_slider.change(
+        a_slider.change(
             fn=plot_function,
-            inputs=[a_slider, b_slider, c_slider, d_slider],
+            inputs=[k_slider, a_slider, b_slider, c_slider],
             outputs=[plot_output],
         )
-        c_slider.change(
+        b_slider.change(
             fn=plot_function,
-            inputs=[a_slider, b_slider, c_slider, d_slider],
+            inputs=[k_slider, a_slider, b_slider, c_slider],
             outputs=[plot_output],
         )
-        d_slider.change(
+        c_slider.change(
             fn=plot_function,
-            inputs=[a_slider, b_slider, c_slider, d_slider],
+            inputs=[k_slider, a_slider, b_slider, c_slider],
             outputs=[plot_output],
         )
 
@@ -522,7 +529,7 @@ def create_gradio_ui():
         demo.load(fn=clear_npz, inputs=None, outputs=None)
         demo.load(
             fn=plot_function,
-            inputs=[a_slider, b_slider, c_slider, d_slider],
+            inputs=[k_slider, a_slider, b_slider, c_slider],
             outputs=[plot_output],
         )