Any interaction refers to the communication between two or more entities (be it abstract/conceptual or physical entity). Successful interaction is equated from the properties of each entity involved in the interaction as well as the capabilities of the interacting entities. With the diversified use and application of computers and specialized devices for specific tasks, such as biomechanical and biomedical devices, interaction design needs to further study the context of the tasks as well. Moreover, with the inclusion of embedded systems and smart devices, instead of focusing only on the hardware performance, the computer architecture needs to consider the opportunities. Especially, HCI can be improved as the current technologies are giving an opportunity for building smart interaction where the user interacts with devices implicitly and in less obtrusive way. In light of this, the design and architecture of an engineered product need to strive for making the product usable and used while making it useful to the user. And this can be achieved if interaction design is dictated by scrutinizing the user model with respects to the usability attributes in view of the context of its task as well as the platform capabilities and constraints as discussed in this chapter.

We analyse inversion of the viscosity ratio M in the Buckley–Leverett equation, distinguishing structural identifiability, observation-operator conditioning, and numerical estimation error. The Riemann solution gives $M=4s^2-4s$ from the shock speed s, with relative condition number $\kappa \left(M\right)=2\sqrt{1+M}/(\sqrt{1+M}-1)$, which diverges as $M\downarrow 0$. The continuum physics objective admits exact solution–parameter pairs for every $M>0$, so identifying the true ratio requires observations. We examine numerical recovery using a viscous physics-informed neural network (PINN) with positive parameterisation and 30 paired repetitions per setting. At $M=3$, the median parameter error decreases from $514.25\%$ without observations to $6.13\%$ with 25 noisy observations. Additional data decrease the median field error, while median parameter errors are nonmonotone. Over $M\in [0.25,10]$, $\kappa$ decreases from $18.94$ to $2.86$, whereas the smooth-branch Cramér–Rao relative scale for 50 scattered observations with $5\%$ Gaussian noise levels off near $7\%$. Shock crossings supply additional nonregular information. Finite-network physics losses remain small across the tested ratios, with different orderings on training and held-out points. Scalar controls assess finite-resolution viscous-model discrepancy; complementary PINN tests show poorer recovery as the front sharpens. Recovery accuracy therefore depends jointly on the observation operator, regularisation, and numerical estimator.

Physics-informed neural networks (PINNs) remain difficult to train for hyperbolic conservation laws. Artificial viscosity is a common remedy, and several methods reduce its coefficient during training. We examine adaptive moment estimation (Adam) followed by limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimisation. The schedule followed during Adam, the viscosity used during L-BFGS, and the checkpoint supplied between them can change together. We separate these factors for the one-dimensional Buckley–Leverett equation using a fixed multilayer perceptron with hyperbolic-tangent activations and 15 paired seeds per configuration. The central experiments impose a zero-diffusive-flux outlet condition. Lowering the L-BFGS viscosity from $3.5\times {10}^{-3}$ to $1.67\times {10}^{-4}$ increased full-grid relative $L^2$ error by $0.0413\pm 0.0069$. The schedule–viscosity interaction was $-0.0067\pm 0.0075$ and was not detected after multiplicity adjustment. A decay ending at $3.5\times {10}^{-3}$ improved on the tested low-endpoint decay before high-viscosity polishing, while its difference from constant high viscosity remained inconclusive. The higher of the two tested constant viscosities improved aggregate and pre-breakthrough accuracy but increased post-breakthrough error. Stage-matched curricula showed no detected accuracy advantage; their greater executed cost arose from intermediate diagnostic L-BFGS phases whose states were discarded. These results identify the terminal viscosity, checkpoint rule, outlet treatment, and optimiser exposure as controls needed to interpret schedule comparisons in this pipeline.