  Avoiding over-pressurization in subsurface reservoirs is critical for
applications like CO2 sequestration and wastewater injection. Managing the
pressures by controlling injection/extraction are challenging because of
complex heterogeneity in the subsurface. The heterogeneity typically requires
high-fidelity physics-based models to make predictions on CO$_2$ fate.
Furthermore, characterizing the heterogeneity accurately is fraught with
parametric uncertainty. Accounting for both, heterogeneity and uncertainty,
makes this a computationally-intensive problem challenging for current
reservoir simulators. To tackle this, we use differentiable programming with a
full-physics model and machine learning to determine the fluid extraction rates
that prevent over-pressurization at critical reservoir locations. We use DPFEHM
framework, which has trustworthy physics based on the standard two-point flux
finite volume discretization and is also automatically differentiable like
machine learning models. Our physics-informed machine learning framework uses
convolutional neural networks to learn an appropriate extraction rate based on
the permeability field. We also perform a hyperparameter search to improve the
model's accuracy. Training and testing scenarios are executed to evaluate the
feasibility of using physics-informed machine learning to manage reservoir
pressures. We constructed and tested a sufficiently accurate simulator that is
400000 times faster than the underlying physics-based simulator, allowing for
near real-time analysis and robust uncertainty quantification.
