This paper introduces a dynamic portfolio optimization framework for large institutional investors using Scientific Physics-Informed Reinforcement Learning (SciPhyRL). Formulated in continuous time over an extended state space that includes explicit cumulative costs, the approach leverages offline historical data to learn optimal, distribution-aware strategies. A core innovation reduces the optimization challenge to solving an HJB equation by projecting it onto observed trajectories as a pathwise Hamilton-Jacobi equation. This is solved directly from data using PINN in a single offline sweep, eliminating the need for traditional value or policy iteration. To make the method effective at practical short horizons, the control variable is recast from a continuous trading rate to a discrete target holding. This ensures signal-implied positions are reached immediately, while execution costs are evaluated against a microstructure-grounded quadratic price impact model. Evaluated on a $14$-asset ETF universe using an engineered oracle signal, the learned Gibbs policy yields substantial out-of-sample Sharpe ratio improvements over static and myopic baselines. The results demonstrate that the proposed framework successfully translates known signal quality into a robust, multi-period, and cost-aware allocation mechanism with strictly controlled volatility and turnover.
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