GSoC Example

examples/IF_brette_multi.py

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+import numpy as np
+from brian2 import *
+from brian2modelfitting import *
+
+'''
+Adaptive exponential IF model introduced by Brette R. and Gerstner W. (2005). The model has 3 distinct firing regiems 
+depending on the parameters used in the simulation. This example shows how multiple sets of parameters can 
+be fitted to the same model simulatenously with the Brian2modelfitting toolbox.
+'''
+
+# Parameters
+C = 281 * pF
+gL = 30 * nS
+taum = C / gL
+EL = -70.6 * mV
+VT = -50.4 * mV
+DeltaT = 2 * mV
+Vcut = VT + 5 * DeltaT
+
+dt = 0.1 * ms
+defaultclock.dt = dt
+
+#Define input current 
+
+input_current1 = np.hstack([np.zeros(int(round(20*ms/dt))),
+                           np.ones(int(round(100*ms/dt))),
+                           np.zeros(int(round(20*ms/dt)))]) * 1
+input_current2 = np.hstack([np.zeros(int(round(20*ms/dt))),
+                           np.ones(int(round(100*ms/dt))),
+                           np.zeros(int(round(20*ms/dt)))]) * 2
+input_current = np.stack((input_current1, input_current2))*nA
+I = TimedArray(input_current.T, dt=dt)
+
+#First simulate the model with known parameters (to obtain data to fit parameters too!). 
+#Define model, setup monitoring & define parameters. 
+
+eqs = """
+dvm/dt = (gL*(EL - vm) + gL*DeltaT*exp((vm - VT)/DeltaT) + I(t, i%2==1) - w)/C : volt
+dw/dt = (a*(vm - EL) - w)/tauw : amp
+tauw : second 
+a : siemens
+b : amp
+Vr : volt
+"""
+
+neuron = NeuronGroup(6, model=eqs, threshold='vm>Vcut',
+                     reset="vm=Vr; w+=b", method='euler')
+neuron.vm = EL
+trace = StateMonitor(neuron, 'vm', record=True)
+spikes = SpikeMonitor(neuron)
+
+neuron.tauw = [144, 144, 20, 20, 144, 144] * ms
+neuron.a = [4*nS, 4*nS, 4*nS, 4*nS, (2*C)/(144*ms), (2*C)/(144*ms)]
+neuron.b = [0.0805, 0.0805, 0.5, 0.5, 0, 0] * nA
+neuron.Vr = [-70.6*mV, -70.6*mV, VT+5*mV, VT+5*mV, -70.6*mV, -70.6*mV]
+
+run(140 * ms) 
+
+spike_train = spikes.spike_trains()
+
+#Put spike spikes and voltage traces into lists , probably lots of smarter ways to do this.
+out_spikes = [[spike_train[0] / second, spike_train[1] /second], [spike_train[2] / second, spike_train[3] / second], [spike_train[4] / second, spike_train[5] / second]]
+v_traces = [[trace.vm[0]/mV, trace.vm[1]/mV], [trace.vm[2]/mV, trace.vm[3]/mV], [trace.vm[4]/mV, trace.vm[5]/mV]]
+
+start_scope()
+
+#Model fitting
+
+eqs_fit = '''
+dvm/dt = (gL*(EL - vm) + gL*DeltaT*exp((vm - VT)/DeltaT) + I - w)/C : volt
+dw/dt = (a*(vm - EL) - w)/tauw : amp
+tauw : second (constant)
+a : siemens (constant)
+b : amp (constant)
+Vr : volt (constant)
+'''
+
+n_opt = NevergradOptimizer()
+metric = GammaFactor(delta=1*ms, time=140*ms)
+
+fitters = []
+for i in range(len(out_spikes)):
+    fitters.append(SpikeFitter(model=eqs_fit, input_var='I', dt=dt,
+                     input=input_current, output=out_spikes[i],
+                     n_samples=800,
+                     param_init={'vm': EL},
+                     threshold='vm > Vcut',
+                     reset='vm=Vr; w+=b',))
+
+result_dict_error = []
+predict_spikes = []
+fits = []
+for fitter in fitters:
+    result_dict_error.append(fitter.fit(n_rounds=15,
+                                    optimizer=n_opt,
+                                    metric=metric,
+                                    callback='progressbar',
+                                    tauw=[1,200]*ms,
+                                    a=[3, 4]*nS, 
+                                    b=[0, 1]*nA,
+                                    Vr=[-80,-40]*mV))
+
+    predict_spikes.append(fitter.generate_spikes(params=None))
+    #print('spike times:', spikes)
+
+    fits.append(fitter.generate(params=None,
+                           output_var='vm'))
+
+#Number of samples (n_samples) and number of epochs (n_rounds) is probably overkill here, can probably be reduced.
+
+#Print parameter results and plot fitted traces
+print(f'Printing fitting results...\n')
+
+for i in range(3):
+    print(f'Results for parameter set {i+1}\n')
+    print(f'tauw (true/predict) : {neuron.tauw[i*2]}, {result_dict_error[i][0]["tauw"]}')
+    print(f'Vr (true/predict) : {neuron.Vr[i*2]}, {result_dict_error[i][0]["Vr"]}')
+    print(f'a (true/predict) : {neuron.a[i*2]}, {result_dict_error[i][0]["a"]}')
+    print(f'b (true/predict) : {neuron.b[i*2]}, {result_dict_error[i][0]["b"]}\n')
+
+fig, ax = plt.subplots(2, 3, figsize=(12, 8))
+
+for i in range(3):
+    ax[0, i].plot(trace.t/ms, v_traces[i][0], label='Simulated');
+    ax[0, i].plot(trace.t/ms, fits[i][0]/mV, label='Fitted');
+    ax[1, i].plot(trace.t/ms, v_traces[i][1]);
+    ax[1, i].plot(trace.t/ms, fits[i][1]/mV);
+
+ax[0, 0].legend()
+ax[0, 0].set_xlabel('Time (ms)')
+ax[0, 0].set_ylabel('v (mV)')
+
+plt.show()