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The deployment of learning-based models in safety-critical control systems demands mathematical guarantees that standard regression architectures cannot provide. This paper presents an integrated framework that bridges Neural Ordinary…
We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…
Presently, there is a steady state approach in Computational fluid dynamics (CFD) to obtain a steady solution directly from the steady state governing equations. Whereas, for obtaining a time-periodic flow solution, the present unsteady…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…
Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…
We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…
Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. In this work, we present a detailed introduction to programming PINN-based computational solid mechanics. Besides, two prevailingly…
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak…
We study elastic snap-through induced by a control parameter that evolves dynamically. In particular, we study an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening…
Persistent Homology (PH) and Artificial Neural Networks (ANNs) offer contrasting approaches to inferring topological structure from data. In this study, we examine the noise robustness of a supervised neural network trained to predict Betti…
Safety validation for Level 4 autonomous vehicles (AVs) is currently bottlenecked by the inability to scale the detection of rare, high-risk long-tail scenarios using traditional rule-based heuristics. We present Deep-Flow, an unsupervised…
Ensuring validation for highly automated driving poses significant obstacles to the widespread adoption of highly automated vehicles. Scenario-based testing offers a potential solution by reducing the homologation effort required for these…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs…
Two-phase flow phenomena underpin critical technologies such as hydrogen fuel cells, spray cooling, and combustion, where droplet dynamics govern performance and efficiency. Conventional optical diagnostics, including shadowgraphy and…
Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of…
Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an…