[BUG]: "Create model from equations" produces/shows wrong models

[liunelson]

Describe the bug

Note:

• in all these cases, the "Edited by AI" equations are all correct.
• since the rate laws are wrong, it seems that the problem lies around the juncture between good LaTeX and MIRA's template_model_from_sympy_odes
• the problem seems to be with sympy.parsing.latex.parse_latex(ode_latex_str) producing incorrect SymPy expressions; example

sympy.parsing.latex.parse_latex(r"\frac{d V(t)}{d t} = a b I(t) (1 - g)")
# produces Eq(Derivative(V(t), t), a*(I(t)*b(1 - g))) where parameter 'b' is treated as a function of (1-g)

sympy.parsing.latex.parse_latex(r"\frac{d I(t)}{d t} = k E(t) - d I(t)")
# produces Eq(Derivative(I(t), t), -dI*t + k*E(t)) where parameter 'd' became 'dI'

• thus, instructing the equation-styling agent to add or retain * in the edited LaTeX as indication of multiplication probably could fix Case 2; currently, the agent is instructed to remove all *
• for Case 3, it seems that the source of the problem is again parse_latex where it adds unnecessary parentheses

sympy.parsing.latex.parse_latex(r"\frac{d I(t)}{d t} = b * S(t) * I(t) - k * g * I(t) - (1 - k) * g * I(t)")
# produces Eq(Derivative(I(t), t), -g*(1 - k)*I(t) + ((b*S(t))*I(t) - g*k*I(t))) where the second term is wrapped in parentheses that MIRA then interprets as a single template

• the solution for Case 1, 3 may be to use a LLM to convert the LaTeX to SymPy with instructions to avoid this sort of parenthesis issue

Case 1

Basic SIR model with added birth and death processes (l birth rate and every state dies at a rate of m)

\frac{d S}{d t} = -b S I + l - m S
\frac{d I}{d t} = b S I - g I - m I
\frac{d R}{d t} = g I - m R

Incorrect model diagram and rate laws:

• https://app.staging.terarium.ai/projects/a1eb1451-35cf-4f39-814d-d1bd46b08360/workflow/d71c39d9-7bb1-4f23-abf2-fa17d4a19a37?operator=72e0d3ba-86bb-43fc-8be6-4531b38b0f43
• there should never be sums in the rate laws
  

Correct model (with its own, unrelated bugs):

• should be 6 templates with rate laws I*S*b, l, S*m, I*g, I*m, R*m
• S is converted to I, I is converted to R, production of S, degradation/death of S, I, R individually
• model1.json, made using Sympy and MIRA directly

odes = [
    sympy.Eq(S(t).diff(t), - b * S(t) * I(t) + l - m * S(t)),
    sympy.Eq(I(t).diff(t), b * S(t) * I(t) - g * I(t) - m * I(t)),
    sympy.Eq(R(t).diff(t), g * I(t) - m * R(t)),
]
model1 = template_model_from_sympy_odes(odes)

Case 2 - Controlled production

Production of viral particles in wastewater (Phan et al. 2023 from last monthly demo)

\frac{d S}{d t} = -l S I
\frac{d E}{d t} = l S I - k E
\frac{d I}{d t} = k E - d I
\frac{d V}{d t} = a b (1 - g) I

Incorrect model:

• https://app.staging.terarium.ai/projects/a1eb1451-35cf-4f39-814d-d1bd46b08360/workflow/d71c39d9-7bb1-4f23-abf2-fa17d4a19a37?operator=1a4058a3-7ef3-4201-a102-fad5c48c7e7c
• the d I(t) term got turned into a natural production with nonsensical rate law -dI * t
• note that renaming the parameter d to f fixes the above point
• the parameter b somehow interpreted as a state variable with d b(t) / d t = 0
• the parameter g disappeared from the rate laws but is somehow still present in the parameter table
• note that changing the equation from a b (1 - g) I(t) to a b I(t) (1 - g) avoids the two above points; this shouldn't matter since SymPy is aware of commutativity (i.e. a b (1 - g) I(t) == a b I(t) (1 - g))
  

Correct model:

• model1b.json
• Made using SymPy and MIRA directly

odes = [
    sympy.Eq(S(t).diff(t), - l * S(t) * I(t)),
    sympy.Eq(E(t).diff(t), l * S(t) * I(t) - k * E(t)),
    sympy.Eq(I(t).diff(t), k * E(t) - d * I(t)),
    sympy.Eq(V(t).diff(t), a * b * (1 - g) * I(t)),
]
model1b = template_model_from_sympy_odes(odes)

Case 3 - Branching ratio (2)

The I state splits into two streams, one into V and other into R.

\frac{d S}{d t} = -b S I
\frac{d I}{d t} = b S I - k g I - (1 - k) g I
\frac{d R}{d t} = k g I
\frac{d V}{d t} = (1 - k) g I

Incorrect model:

• https://app.staging.terarium.ai/projects/a1eb1451-35cf-4f39-814d-d1bd46b08360/workflow/d71c39d9-7bb1-4f23-abf2-fa17d4a19a37?operator=58f24dd2-f09e-421d-a426-2dcfeff60482
• templates t1, t3 are completely wrong - should be a single controlled conversion from S to I with rate law I*S*b
• template t4 is supposed to be a natural conversion from I to R with rate law I*g*k
  

Correct model:

• model2a.json
• Made with this SymPy and MIRA

odes = [
    sympy.Eq(S(t).diff(t), - b * S(t) * I(t)),
    sympy.Eq(I(t).diff(t), b * S(t) * I(t) - k * g * I(t) - (1 - k) * g * I(t)),
    sympy.Eq(R(t).diff(t), k * g * I(t)),
    sympy.Eq(V(t).diff(t), (1 - k) * g * I(t))
]
model2a = template_model_from_sympy_odes(odes)

[liunelson]

Now that I think of it, as in the "Note" above, we maybe forced to create a GoLLM task to convert the cleaned LaTeX to SymPy since most of the cases are due to extra () introduced by SymPy's parse_latex.