Intravesical adoptive cell therapy (ACT) with tumor-infiltrating lymphocytes (TIL) holds promise for durable responses in bladder cancer by administering TILs locally, thus maximizing T cells numbers in the tumor area. However, T cells in the bladder encounter an immunosuppressive population of stromal cells such as myeloid-derived suppressor cells (MDSCs), that can weaken T cell responses. Intravesical delivery of gemcitabine acts as a local lymphodepletion agent, which preconditions the bladder microenvironment for the infused T cells. To understand the underlying biological mechanisms and optimize T cell response, we employ the physics-informed neural network (PINN), with an adaptive loss weighting following the multi-task learning of the objective function to balance the contributions of the different loss terms. Using a pre-clinical murine model, bladder tumor growth was measured via ultrasound, and mice were separated into untreated, gemcitabine only (GEM), OT-I only (OT-I), and combination (GEM + OT-I) groups. An ordinary differential equation (ODE) model of tumor cells, T cells, and MDSCs interactions under the 4 different treatments is used to study the changing interactions over time between the different cells and their response to a combination of anticancer treatments. Biological constraints are enforced on the tumor cells, T cells, and MDSCs using a two-time-point histology data. We learn possible trajectories of the different interacting cells at time points where no observed data are available. We infer time-varying interactions between cells, and their response to a combination of anticancer treatments and describe its underlying implication for the biological mechanism of T cell response.