Welcome to the Forum. I am not sure I understand the nature of the issue, but some reflections below.
> certain modes are only coming and overpowering the results by making the model behave erratically.
That sounds like you may be (freely) optimising the modal mix. If you are using a bottom-up energy system model like TIMES, such models are, in general, best suited for the analysis of the development of the technology mix serving each demand mode (over the full energy/supply chain), and the related impacts on e.g. energy and emissions balances. Therefore, many of these models simply employ
exogenous projections for the modal demands, with own-price demand elasticities in policy scenarios. Impacts of modal shifts can be modelled by scenarios (each having different exogenous projections), but indeed they can also be modelled endogenously. However, endogenous modal shifting is a somewhat more delicate modelling issue, and requires careful consideration of the infrastructure costs, behavioural aspects such as intangible costs (e.g. travel time budgets), and/or substitution elasticities.
> Specifically, cost_activity is coming lower and we are unable to understand where the potential issue might be in the demand inputs.
Yes, if you are letting the model freely optimize the travel modes, something like that would be the likely outcome: cheapest cost modes would be winning the markets.
As indicated above, you can indeed model modal shifts also endogenously by incorporating intangible costs (e.g. travel time budgets), together with a careful Baseline calibration, or by using CES-like substitution elasticities in the policy scenarios. For the travel time budget approach, see e.g. the following ETSAP project report:
Modal Choice in a TIMES Model.