Alessandro Alla

Physics-Informed Neural Networks (PINNs) have revolutionized solving differential equations by integrating physical laws into neural networks training. This paper explores PINNs for open-loop optimal control problems with incomplete information, such as sparse initial and boundary data and partially unknown system parameters. We derive optimality conditions from the Lagrangian multipliers and use PINNs to predict the state, adjoint, and control variables. In contrast with previous methods, our approach integrates these elements into a single neural network and addresses scenarios with consistently limited data. In addition, we address the study of partially unknown equations identifying underlying parameters online by searching for the optimal solution recurring to a 2-in-series architecture of PINNs, in which scattered data of the uncontrolled solution is used. Numerical examples show the effectiveness of the proposed method even in scenarios characterized by a considerable lack of information.

Ionic transition metal complexes (iTMCs) often suffer from low photoluminescence quantum yield, especially in the red to near‐infrared spectral region. Rational molecular design strategies unlock recovering the emission features efficiently. A potential solution is offered by bimetallic complexes, which are rapidly emerging as a valid and attractive class of emitters. In this work, the yet unexplored electrochemiluminescence (ECL) properties of a series of heterobimetallic complexes of general structure Ir ^III ‐M ^I are investigated, where the formally neutral cyclometalated iridium complex provides efficient photo‐ and electro‐active properties to the molecular emitters. Whereas bulky M ^I (gold or copper) metalloligand increases structural rigidity and chemical stability of the architecture while enabling larger values for the radiative rate constant. The Ir ^III ‐M ^I shows highly efficient red ECL at λ _{em , max} = 600 nm, which is stable in a wider range of applied potential. The activation is triggered at 0.45–0.65 V, ca. 0.3–0.5 V lower than that of tris ‐(2,2′‐bipyridyl) ruthenium(II) complex, [Ru(bpy) ₃ ] ²⁺ . Remarkably, the ECL quantum yield relative to [Ru(bpy) ₃ ] ²⁺ is up to six‐fold higher, thus positioning this new series of iTMCs amongst the brightest ECL‐active emitters to date and possibly offering a platform to develop novel and even more efficient ECL probes for biosensing and bioimaging applications.