Added FeynmanEquations Dataset and Problems for testing

datasets/FeynmanEquations.csv

@@ -0,0 +1,101 @@
+Filename,datapoints,Number,Output,Formula,# variables,v1_name,v1_low,v1_high,v2_name,v2_low,v2_high,v3_name,v3_low,v3_high,v4_name,v4_low,v4_high,v5_name,v5_low,v5_high,v6_name,v6_low,v6_high,v7_name,v7_low,v7_high,v8_name,v8_low,v8_high,v9_name,v9_low,v9_high,v10_name,v10_low,v10_high
+I.6.2a,10,1,f,exp(-theta**2/2)/sqrt(2*pi),1,theta,1,3,,,,,,,,,,,,,,,,,,,,,,,,,,,
+I.6.2,100,2,f,exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma),2,sigma,1,3,theta,1,3,,,,,,,,,,,,,,,,,,,,,,,,
+I.6.2b,1000,3,f,exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma),3,sigma,1,3,theta,1,3,theta1,1,3,,,,,,,,,,,,,,,,,,,,,
+I.8.14,100,4,d,sqrt((x2-x1)**2+(y2-y1)**2),4,x1,1,5,x2,1,5,y1,1,5,y2,1,5,,,,,,,,,,,,,,,,,,
+I.9.18,1000000,5,F,G*m1*m2/((x2-x1)**2+(y2-y1)**2+(z2-z1)**2),9,m1,1,2,m2,1,2,G,1,2,x1,3,4,x2,1,2,y1,3,4,y2,1,2,z1,3,4,z2,1,2,,,
+I.10.7,10,6,m,m_0/sqrt(1-v**2/c**2),3,m_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
+I.11.19,100,7,A,x1*y1+x2*y2+x3*y3,6,x1,1,5,x2,1,5,x3,1,5,y1,1,5,y2,1,5,y3,1,5,,,,,,,,,,,,
+I.12.1,10,8,F,mu*Nn,2,mu,1,5,Nn,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+I.12.2,10,10,F,q1*q2*r/(4*pi*epsilon*r**3),4,q1,1,5,q2,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,
+I.12.4,10,11,Ef,q1*r/(4*pi*epsilon*r**3),3,q1,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
+I.12.5,10,12,F,q2*Ef,2,q2,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+I.12.11,10,13,F,q*(Ef+B*v*sin(theta)),5,q,1,5,Ef,1,5,B,1,5,v,1,5,theta,1,5,,,,,,,,,,,,,,,
+I.13.4,10,9,K,1/2*m*(v**2+u**2+w**2),4,m,1,5,v,1,5,u,1,5,w,1,5,,,,,,,,,,,,,,,,,,
+I.13.12,10,14,U,G*m1*m2*(1/r2-1/r1),5,m1,1,5,m2,1,5,r1,1,5,r2,1,5,G,1,5,,,,,,,,,,,,,,,
+I.14.3,10,15,U,m*g*z,3,m,1,5,g,1,5,z,1,5,,,,,,,,,,,,,,,,,,,,,
+I.14.4,10,16,U,1/2*k_spring*x**2,2,k_spring,1,5,x,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+I.15.3x,10,17,x1,(x-u*t)/sqrt(1-u**2/c**2),4,x,5,10,u,1,2,c,3,20,t,1,2,,,,,,,,,,,,,,,,,,
+I.15.3t,100,18,t1,(t-u*x/c**2)/sqrt(1-u**2/c**2),4,x,1,5,c,3,10,u,1,2,t,1,5,,,,,,,,,,,,,,,,,,
+I.15.1,10,19,p,m_0*v/sqrt(1-v**2/c**2),3,m_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
+I.16.6,10,20,v1,(u+v)/(1+u*v/c**2),3,c,1,5,v,1,5,u,1,5,,,,,,,,,,,,,,,,,,,,,
+I.18.4,10,21,r,(m1*r1+m2*r2)/(m1+m2),4,m1,1,5,m2,1,5,r1,1,5,r2,1,5,,,,,,,,,,,,,,,,,,
+I.18.12,10,22,tau,r*F*sin(theta),3,r,1,5,F,1,5,theta,0,5,,,,,,,,,,,,,,,,,,,,,
+I.18.14,10,23,L,m*r*v*sin(theta),4,m,1,5,r,1,5,v,1,5,theta,1,5,,,,,,,,,,,,,,,,,,
+I.24.6,10,24,E_n,1/2*m*(omega**2+omega_0**2)*1/2*x**2,4,m,1,3,omega,1,3,omega_0,1,3,x,1,3,,,,,,,,,,,,,,,,,,
+I.25.13,10,25,Volt,q/C,2,q,1,5,C,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+I.26.2,100,26,theta1,arcsin(n*sin(theta2)),2,n,0,1,theta2,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+I.27.6,10,27,foc,1/(1/d1+n/d2),3,d1,1,5,d2,1,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
+I.29.4,10,28,k,omega/c,2,omega,1,10,c,1,10,,,,,,,,,,,,,,,,,,,,,,,,
+I.29.16,1000,29,x,sqrt(x1**2+x2**2-2*x1*x2*cos(theta1-theta2)),4,x1,1,5,x2,1,5,theta1,1,5,theta2,1,5,,,,,,,,,,,,,,,,,,
+I.30.3,100,30,Int,Int_0*sin(n*theta/2)**2/sin(theta/2)**2,3,Int_0,1,5,theta,1,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
+I.30.5,100,31,theta,arcsin(lambd/(n*d)),3,lambd,1,2,d,2,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
+I.32.5,10,32,Pwr,q**2*a**2/(6*pi*epsilon*c**3),4,q,1,5,a,1,5,epsilon,1,5,c,1,5,,,,,,,,,,,,,,,,,,
+I.32.17,10,33,Pwr,(1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2),6,epsilon,1,2,c,1,2,Ef,1,2,r,1,2,omega,1,2,omega_0,3,5,,,,,,,,,,,,
+I.34.8,10,34,omega,q*v*B/p,4,q,1,5,v,1,5,B,1,5,p,1,5,,,,,,,,,,,,,,,,,,
+I.34.1,10,35,omega,omega_0/(1-v/c),3,c,3,10,v,1,2,omega_0,1,5,,,,,,,,,,,,,,,,,,,,,
+I.34.14,10,36,omega,(1+v/c)/sqrt(1-v**2/c**2)*omega_0,3,c,3,10,v,1,2,omega_0,1,5,,,,,,,,,,,,,,,,,,,,,
+I.34.27,10,37,E_n,(h/(2*pi))*omega,2,omega,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+I.37.4,100,38,Int,I1+I2+2*sqrt(I1*I2)*cos(delta),3,I1,1,5,I2,1,5,delta,1,5,,,,,,,,,,,,,,,,,,,,,
+I.38.12,10,39,r,4*pi*epsilon*(h/(2*pi))**2/(m*q**2),4,m,1,5,q,1,5,h,1,5,epsilon,1,5,,,,,,,,,,,,,,,,,,
+I.39.1,10,40,E_n,3/2*pr*V,2,pr,1,5,V,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+I.39.11,10,41,E_n,1/(gamma-1)*pr*V,3,gamma,2,5,pr,1,5,V,1,5,,,,,,,,,,,,,,,,,,,,,
+I.39.22,10,42,pr,n*kb*T/V,4,n,1,5,T,1,5,V,1,5,kb,1,5,,,,,,,,,,,,,,,,,,
+I.40.1,10,43,n,n_0*exp(-m*g*x/(kb*T)),6,n_0,1,5,m,1,5,x,1,5,T,1,5,g,1,5,kb,1,5,,,,,,,,,,,,
+I.41.16,10,44,L_rad,h/(2*pi)*omega**3/(pi**2*c**2*(exp((h/(2*pi))*omega/(kb*T))-1)),5,omega,1,5,T,1,5,h,1,5,kb,1,5,c,1,5,,,,,,,,,,,,,,,
+I.43.16,10,45,v,mu_drift*q*Volt/d,4,mu_drift,1,5,q,1,5,Volt,1,5,d,1,5,,,,,,,,,,,,,,,,,,
+I.43.31,10,46,D,mob*kb*T,3,mob,1,5,T,1,5,kb,1,5,,,,,,,,,,,,,,,,,,,,,
+I.43.43,10,47,kappa,1/(gamma-1)*kb*v/A,4,gamma,2,5,kb,1,5,A,1,5,v,1,5,,,,,,,,,,,,,,,,,,
+I.44.4,10,48,E_n,n*kb*T*ln(V2/V1),5,n,1,5,kb,1,5,T,1,5,V1,1,5,V2,1,5,,,,,,,,,,,,,,,
+I.47.23,10,49,c,sqrt(gamma*pr/rho),3,gamma,1,5,pr,1,5,rho,1,5,,,,,,,,,,,,,,,,,,,,,
+I.48.2,100,50,E_n,m*c**2/sqrt(1-v**2/c**2),3,m,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
+I.50.26,10,51,x,x1*(cos(omega*t)+alpha*cos(omega*t)**2),4,x1,1,3,omega,1,3,t,1,3,alpha,1,3,,,,,,,,,,,,,,,,,,
+II.2.42,10,52,Pwr,kappa*(T2-T1)*A/d,5,kappa,1,5,T1,1,5,T2,1,5,A,1,5,d,1,5,,,,,,,,,,,,,,,
+II.3.24,10,53,flux,Pwr/(4*pi*r**2),2,Pwr,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+II.4.23,10,54,Volt,q/(4*pi*epsilon*r),3,q,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
+II.6.11,10,55,Volt,1/(4*pi*epsilon)*p_d*cos(theta)/r**2,4,epsilon,1,3,p_d,1,3,theta,1,3,r,1,3,,,,,,,,,,,,,,,,,,
+II.6.15a,1000,56,Ef,p_d/(4*pi*epsilon)*3*z/r**5*sqrt(x**2+y**2),6,epsilon,1,3,p_d,1,3,r,1,3,x,1,3,y,1,3,z,1,3,,,,,,,,,,,,
+II.6.15b,10,57,Ef,p_d/(4*pi*epsilon)*3*cos(theta)*sin(theta)/r**3,4,epsilon,1,3,p_d,1,3,theta,1,3,r,1,3,,,,,,,,,,,,,,,,,,
+II.8.7,10,58,E_n,3/5*q**2/(4*pi*epsilon*d),3,q,1,5,epsilon,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
+II.8.31,10,59,E_den,epsilon*Ef**2/2,2,epsilon,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+II.10.9,10,60,Ef,sigma_den/epsilon*1/(1+chi),3,sigma_den,1,5,epsilon,1,5,chi,1,5,,,,,,,,,,,,,,,,,,,,,
+II.11.3,10,61,x,q*Ef/(m*(omega_0**2-omega**2)),5,q,1,3,Ef,1,3,m,1,3,omega_0,3,5,omega,1,2,,,,,,,,,,,,,,,
+II.11.17,10,62,n,n_0*(1+p_d*Ef*cos(theta)/(kb*T)),6,n_0,1,3,kb,1,3,T,1,3,theta,1,3,p_d,1,3,Ef,1,3,,,,,,,,,,,,
+II.11.20,10,63,Pol,n_rho*p_d**2*Ef/(3*kb*T),5,n_rho,1,5,p_d,1,5,Ef,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,
+II.11.27,100,64,Pol,n*alpha/(1-(n*alpha/3))*epsilon*Ef,4,n,0,1,alpha,0,1,epsilon,1,2,Ef,1,2,,,,,,,,,,,,,,,,,,
+II.11.28,100,65,theta,1+n*alpha/(1-(n*alpha/3)),2,n,0,1,alpha,0,1,,,,,,,,,,,,,,,,,,,,,,,,
+II.13.17,10,66,B,1/(4*pi*epsilon*c**2)*2*I/r,4,epsilon,1,5,c,1,5,I,1,5,r,1,5,,,,,,,,,,,,,,,,,,
+II.13.23,100,67,rho_c,rho_c_0/sqrt(1-v**2/c**2),3,rho_c_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
+II.13.34,10,68,j,rho_c_0*v/sqrt(1-v**2/c**2),3,rho_c_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
+II.15.4,10,69,E_n,-mom*B*cos(theta),3,mom,1,5,B,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
+II.15.5,10,70,E_n,-p_d*Ef*cos(theta),3,p_d,1,5,Ef,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
+II.21.32,10,71,Volt,q/(4*pi*epsilon*r*(1-v/c)),5,q,1,5,epsilon,1,5,r,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,
+II.24.17,10,72,k,sqrt(omega**2/c**2-pi**2/d**2),3,omega,4,6,c,1,2,d,2,4,,,,,,,,,,,,,,,,,,,,,
+II.27.16,10,73,flux,epsilon*c*Ef**2,3,epsilon,1,5,c,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,
+II.27.18,10,74,E_den,epsilon*Ef**2,2,epsilon,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+II.34.2a,10,75,I,q*v/(2*pi*r),3,q,1,5,v,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
+II.34.2,10,76,mom,q*v*r/2,3,q,1,5,v,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
+II.34.11,10,77,omega,g_*q*B/(2*m),4,g_,1,5,q,1,5,B,1,5,m,1,5,,,,,,,,,,,,,,,,,,
+II.34.29a,10,78,mom,q*h/(4*pi*m),3,q,1,5,h,1,5,m,1,5,,,,,,,,,,,,,,,,,,,,,
+II.34.29b,10,79,E_n,g_*mom*B*Jz/(h/(2*pi)),5,g_,1,5,h,1,5,Jz,1,5,mom,1,5,B,1,5,,,,,,,,,,,,,,,
+II.35.18,10,80,n,n_0/(exp(mom*B/(kb*T))+exp(-mom*B/(kb*T))),5,n_0,1,3,kb,1,3,T,1,3,mom,1,3,B,1,3,,,,,,,,,,,,,,,
+II.35.21,10,81,M,n_rho*mom*tanh(mom*B/(kb*T)),5,n_rho,1,5,mom,1,5,B,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,
+II.36.38,10,82,f,mom*H/(kb*T)+(mom*alpha)/(epsilon*c**2*kb*T)*M,8,mom,1,3,H,1,3,kb,1,3,T,1,3,alpha,1,3,epsilon,1,3,c,1,3,M,1,3,,,,,,
+II.37.1,10,83,E_n,mom*(1+chi)*B,3,mom,1,5,B,1,5,chi,1,5,,,,,,,,,,,,,,,,,,,,,
+II.38.3,10,84,F,Y*A*x/d,4,Y,1,5,A,1,5,d,1,5,x,1,5,,,,,,,,,,,,,,,,,,
+II.38.14,10,85,mu_S,Y/(2*(1+sigma)),2,Y,1,5,sigma,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+III.4.32,10,86,n,1/(exp((h/(2*pi))*omega/(kb*T))-1),4,h,1,5,omega,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,,,,
+III.4.33,10,87,E_n,(h/(2*pi))*omega/(exp((h/(2*pi))*omega/(kb*T))-1),4,h,1,5,omega,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,,,,
+III.7.38,10,88,omega,2*mom*B/(h/(2*pi)),3,mom,1,5,B,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,
+III.8.54,10,89,prob,sin(E_n*t/(h/(2*pi)))**2,3,E_n,1,2,t,1,2,h,1,4,,,,,,,,,,,,,,,,,,,,,
+III.9.52,1000,90,prob,(p_d*Ef*t/(h/(2*pi)))*sin((omega-omega_0)*t/2)**2/((omega-omega_0)*t/2)**2,6,p_d,1,3,Ef,1,3,t,1,3,h,1,3,omega,1,5,omega_0,1,5,,,,,,,,,,,,
+III.10.19,100,91,E_n,mom*sqrt(Bx**2+By**2+Bz**2),4,mom,1,5,Bx,1,5,By,1,5,Bz,1,5,,,,,,,,,,,,,,,,,,
+III.12.43,10,92,L,n*(h/(2*pi)),2,n,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,,,,
+III.13.18,10,93,v,2*E_n*d**2*k/(h/(2*pi)),4,E_n,1,5,d,1,5,k,1,5,h,1,5,,,,,,,,,,,,,,,,,,
+III.14.14,10,94,I,I_0*(exp(q*Volt/(kb*T))-1),5,I_0,1,5,q,1,2,Volt,1,2,kb,1,2,T,1,2,,,,,,,,,,,,,,,
+III.15.12,10,95,E_n,2*U*(1-cos(k*d)),3,U,1,5,k,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
+III.15.14,10,96,m,(h/(2*pi))**2/(2*E_n*d**2),3,h,1,5,E_n,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
+III.15.27,10,97,k,2*pi*alpha/(n*d),3,alpha,1,5,n,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
+III.17.37,10,98,f,beta*(1+alpha*cos(theta)),3,beta,1,5,alpha,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
+III.19.51,10,99,E_n,-m*q**4/(2*(4*pi*epsilon)**2*(h/(2*pi))**2)*(1/n**2),5,m,1,5,q,1,5,h,1,5,n,1,5,epsilon,1,5,,,,,,,,,,,,,,,
+III.21.20,10,100,j,-rho_c_0*q*A_vec/m,4,rho_c_0,1,5,q,1,5,A_vec,1,5,m,1,5,,,,,,,,,,,,,,,,,,

pysr/Problems.py

@@ -0,0 +1,90 @@
+import numpy as np
+import pandas as pd
+import tempfile, os, pdb, csv, traceback,random, time
+
+
+class Problem:
+    """
+    Problem API to work with PySR.
+
+    Should be able to call pysr(problem.X, problem.y, var_names=problem.var_names) and have it work
+    """
+    def __init__(self, X, y, var_names=None):
+        self.X = X
+        self.y = y
+        self.var_names = var_names
+
+
+class FeynmanProblem(Problem):
+    """
+    Stores the data for the problems from the 100 Feynman Equations on Physics.
+    This is the benchmark used in the AI Feynman Paper
+    """
+    def __init__(self, row, gen=False, dp=500):
+        """
+        row: a row read as a dict from the FeynmanEquations dataset provided in the datasets folder of the repo
+        gen: If true the problem will have dp X and y values randomly generated else they will be None
+        """
+        self.eq_id      = row['Filename']
+        self.form       = row['Formula']
+        self.n_vars     = int(row['# variables'])
+        super(FeynmanProblem, self).__init__(None, None, var_names=[row[f'v{i + 1}_name'] for i in range(self.n_vars)])
+        #self.var_names  = [row[f'v{i+1}_name']  for i in range(self.n_vars)]
+        self.low        = [float(row[f'v{i+1}_low'])   for i in range(self.n_vars)]
+        self.high       = [float(row[f'v{i+1}_high'])  for i in range(self.n_vars)]
+        self.dp         = dp#int(row[f'datapoints'])
+        #self.X = None
+        #self.Y = None
+        if gen:
+            self.X = np.random.uniform(0.01, 25, size=(self.dp, self.n_vars))
+            d = {}
+            for var in range(len(self.var_names)):
+                d[self.var_names[var]] = self.X[:, var]
+            d['exp'] = np.exp
+            d['sqrt'] = np.sqrt
+            d['pi'] = np.pi
+            d['cos'] = np.cos
+            d['sin'] = np.sin
+            d['tan'] = np.tan
+            d['tanh'] = np.tanh
+            d['ln']   = np.log
+            d['log'] = np.log # Quite sure the Feynman dataset has no base 10 logs
+            d['arcsin'] = np.arcsin
+            self.Y = eval(self.form,d)
+        return
+
+    def __str__(self):
+        return f"Feynman Equation: {self.eq_id}|Form: {self.form}"
+
+    def __repr__(self):
+        return str(self)
+
+    def mk_problems(first=100, gen=False, dp=500, data_dir="datasets/FeynmanEquations.csv"):
+        """
+
+        first: the first "first" equations from the dataset will be made into problems
+        data_dir: the path pointing to the Feynman Equations csv
+        returns: list of FeynmanProblems
+        """
+        ret = []
+        with open(data_dir) as csvfile:
+            ind = 0
+            reader = csv.DictReader(csvfile)
+            for i, row in enumerate(reader):
+                if ind > first:
+                    break
+                if row['Filename'] == '': continue
+                try:
+                    p = FeynmanProblem(row, gen=gen, dp=dp)
+                    ret.append(p)
+                except Exception as e:
+                    #traceback.print_exc()
+                    #print(row)
+                    print(f"FAILED ON ROW {i}")
+                ind += 1
+        return ret
+
+
+if __name__ == "__main__":
+    ret = FeynmanProblem.mk_problems(first=100, gen=True)
+    print(ret)