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Implicit Neural Representations (INRs) are powerful to parameterize continuous signals in computer vision. However, almost all INRs methods are limited to low-level tasks, e.g., image/video compression, super-resolution, and image…

Deep neural networks are frequently used by autonomous systems for their ability to learn complex, non-linear data patterns and make accurate predictions in dynamic environments. However, their use as black boxes introduces risks as the…

Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization…

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

The recent decade has seen an enormous rise in the popularity of deep learning and neural networks. These algorithms have broken many previous records and achieved remarkable results. Their outstanding performance has significantly sped up…

We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs).…

Machine learning interatomic potentials (MLIPs) are promising surrogates for quantum mechanics evaluations in ab-initio molecular dynamics simulations due to their ability to reproduce the energy and force landscape within chemical accuracy…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the…

In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and…

The capability of making interpretable and self-explanatory decisions is essential for developing responsible machine learning systems. In this work, we study the learning to explain problem in the scope of inductive logic programming…

Intrusion Detection Systems (IDSs) must maintain high detection sensitivity while operating under strict false-positive constraints, a challenge intensified by class imbalance and heterogeneous IoT traffic. This work investigates whether…

Deep learning-based numerical schemes for solving high-dimensional backward stochastic differential equations (BSDEs) have recently raised plenty of scientific interest. While they enable numerical methods to approximate very…

Quantum many-body problems are central to various scientific disciplines, yet their ground-state properties are intrinsically challenging to estimate. Recent advances in deep learning (DL) offer potential solutions in this field,…

On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and…

Nonlinear system identification often involves a fundamental trade-off between interpretability and flexibility, often requiring the incorporation of physical constraints. We propose a unified data-driven framework that combines the…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have…

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…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…