Decentralized Exchanges are rapidly changing financial markets by using blockchain technology to eliminate intermediaries. They operate through Automated Market Makers (AMMs) and liquidity pools, thereby enabling users to provide or take liquidity. Among others, Uniswap v3 is the most prominent due to the Concentrated Liquidity mechanism, which allows Liquidity Providers to allocate their capital within flexible price ranges, thus increasing possible revenues. This feature brings a key trade-off: narrower ranges increase both potential returns and the risk of inactive liquidity; wider ranges ensure continuous but lower profits. The liquidity provision problem so far discussed is becoming a crucial problem both in the industry and academia. Indeed, several papers face this phenomenon from different points of view. We contribute to this discussion by proposing a novel framework for evaluating and optimizing a liquidity provision position in Uniswap v3. Specifically, let's assume our perspective starts at time t=0. The value of the LP's position at a future time T can be regarded as a random variable depending on the choice of the provision range. A standard approach in mathematical finance maximizes the expected utility associated with this random variable, specifically the mean-variance utility function. The assumptions leading to the Stochastic Differential Equation describing the evolution of the pool should reflect the agent's beliefs and opinions about the state of the market. Next, the expected utility is obtained using the Feynman-Kac theorem and the Physics Informed Neural Network to solve the corresponding Partial Differential Equation. Still, the neural network computing the expected utility depends on the choice of the provision range. At this time, a standard maximization algorithm can be used to maximize the neural network output, thus finding the optimal range. As the main computational load of the neural network is in the offline training step, our methodology benefits from being computationally efficient in the online evaluation step concerning the optimization, where multiple evaluations have to be performed on a short time interval. Finally, our proposal is tested using two standard benchmarks, which are the Black-Scholes and Heston models. As a baseline, we use the liquidity provision strategy that does not exploit the power of concentrated liquidity. The experimental results assess the efficiency of the suggested scheme.