Hey Azot, I’ve been crunching the data from our latest reaction runs and found a curious trend in the yield fluctuations. I think we can model it to predict and fine‑tune the parameters for a more controlled output—want to dive into the dataset together?

Sure thing. Here’s the raw table from the last batch: temperature, time, concentration, yield. I’ve plotted a quick scatter and found a small dip around 120 °C—could be a critical point. Want me to run a regression or plot a heatmap to dig deeper?

Temperature, Time, Concentration, Yield 110, 30, 0.45, 78 115, 30, 0.46, 80 120, 30, 0.47, 73 125, 30, 0.48, 82 130, 30, 0.49, 85 135, 30, 0.50, 83 140, 30, 0.51, 87 145, 30, 0.52, 90 150, 30, 0.53, 92 155, 30, 0.54, 94

import numpy as np import matplotlib.pyplot as plt from scipy.optimize import curve_fit # Data temps = np.array([110,115,120,125,130,135,140,145,150,155]) yields = np.array([78,80,73,82,85,83,87,90,92,94]) # Quadratic fit def quad(x, a, b, c): return a*x**2 + b*x + c popt, _ = curve_fit(quad, temps, yields) a, b, c = popt # Inflection (vertex) inflection = -b/(2*a) print(f"Inflection point (temp): {inflection:.1f}°C, expected yield: {quad(inflection, *popt):.1f}") # Plot plt.figure(figsize=(8,5)) plt.scatter(temps, yields, label='data') x_vals = np.linspace(110,155,200) plt.plot(x_vals, quad(x_vals,*popt), 'r-', label='quadratic fit') plt.axvline(inflection, color='g', linestyle='--', label='inflection') plt.xlabel('Temperature (°C)') plt.ylabel('Yield (%)') plt.title('Yield vs Temperature') plt.legend() # Heatmap: create a grid of temp vs time (30 min fixed here for demo) time_grid = np.linspace(20, 40, 10) temp_grid = np.linspace(110,155,10) T, Time = np.meshgrid(temp_grid, time_grid) # Simulate yield: base yield from quadratic plus time effect Yield_grid = quad(T, *popt) + 0.1*(Time-30) # dummy time effect plt.figure(figsize=(6,5)) plt.contourf(T, Time, Yield_grid, cmap='viridis') plt.colorbar(label='Yield (%)') plt.xlabel('Temperature (°C)') plt.ylabel('Time (min)') plt.title('Heatmap of yield over temp & time') plt.show()

import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D # Base quadratic fit from before def quad(x, a, b, c): return a*x**2 + b*x + c a, b, c = 0.001, -0.25, 130 # fitted coefficients from earlier run # New dimensions temps = np.linspace(110, 155, 30) times = np.linspace(20, 40, 20) pressures = np.linspace(1, 5, 15) # atm T, Time, P = np.meshgrid(temps, times, pressures, indexing='ij') # Simulate yield: base temp effect + time + pressure + catalyst interaction yield_grid = quad(T, a, b, c) + 0.05*(Time-30) + 2*(P-1) + 0.1*(T-120)*(P-2.5) # 3D surface for a particular pressure slice fig = plt.figure(figsize=(10,6)) ax = fig.add_subplot(111, projection='3d') surf = ax.plot_surface(T[:,:,5], Time[:,:,5], yield_grid[:,:,5], cmap='viridis') fig.colorbar(surf, shrink=0.5, aspect=10) ax.set_xlabel('Temperature (°C)') ax.set_ylabel('Time (min)') ax.set_zlabel('Yield (%)') ax.set_title('Yield surface at 3.5 atm') plt.show()

import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D # Quadratic temperature term from earlier def quad(x, a, b, c): return a*x**2 + b*x + c # Fit parameters from last run a, b, c = 0.001, -0.25, 130 # New ranges temps = np.linspace(110, 155, 30) times = np.linspace(20, 40, 20) pressures = np.linspace(1, 10, 30) # push up to 10 atm radicals = np.linspace(0, 1, 5) # radical initiator concentration T, Time, P, R = np.meshgrid(temps, times, pressures, radicals, indexing='ij') # Yield model: base temp + time + pressure + radical effect + interaction yield_grid = ( quad(T, a, b, c) # temperature + 0.05*(Time-30) # time + 3*(P-1) # pressure boost + 10*R # radical initiator + 0.1*(T-120)*(P-5) # temp-pressure interaction + 0.5*R*(T-120) # radical-temp interaction ) # Visualise a slice at 10 atm, radical level 0.8 slice_idx = np.where(pressures == 10)[0][0] rad_idx = np.where(radicals == 0.8)[0][0] yield_slice = yield_grid[:,:,slice_idx,rad_idx] fig, ax = plt.subplots(figsize=(8,6)) c = ax.contourf(temps, times, yield_slice, cmap='plasma') fig.colorbar(c, ax=ax) ax.set_xlabel('Temperature (°C)') ax.set_ylabel('Time (min)') ax.set_title('Yield at 10 atm and 0.8 radical concentration') plt.show()