I NPUT S PECIFIC N EURAL N ETWORKS A P REPRINT Asghar Jadoon The University of Texas at Austin Austin TX, USA D. Thomas Seidl Sandia National Laboratories Albuquerque NM, USA Reese E. Jones Sandia National Laboratories Livermore CA, USA Jan Fuhg The University of Texas at Austin Austin TX, USA February 2025 Abstract Neural networks have emerged as powerful tools for mapping between inputs and outputs. However, their black-box nature limits the ability to encode or impose specific structural relationships between inputs and outputs. While various studies have introduced architectures that ensure the network's output adheres to a particular form in relation to certain inputs, the majority of these approaches impose constraints on only a single set of inputs, leaving others unconstrained. This paper introduces a novel neural network architecture, termed the Input Specific Neural Network (ISNN), which extends this concept by allowing scalar-valued outputs to be subject to multiple constraints. Specifically, the ISNN can enforce convexity in some inputs, non-decreasing monotonicity combined with convexity with respect to others, and simple non-decreasing monotonicity or arbitrary relationships with additional inputs. To the best of our knowledge, this is the first work that proposes a framework that simultaneously comprehensively imposes all these constraints. The paper presents two distinct ISNN architectures, along with equations for the first and second derivatives of the output with respect to the inputs. These networks are broadly applicable. In this work, we restrict their usage to solving problems in computational mechanics. In particular, we show how they can be effectively applied to fitting data-driven constitutive models. We remark, that due to their increased ability to implicitly model constraints, we can show that ISNNs require fewer inputs than existing input convex neural networks when modeling polyconvex hyperelastic functions. We then embed our trained data-driven constitutive laws into a finite element solver where significant time savings can be achieved by using explicit manual differentiation using the derived equations as opposed to automatic differentiation. Manual differentiation also enables seamless employment of trained ISNNs in commercial solvers where automatic differentiation may not be possible. We also show how ISNNs can be used to learn structural relationships between inputs and outputs via a binary gating mechanism.

The approaches are very secure, however, the computational complexity of decryption is generally Deep neural networks (DNNs) show prominent superiority in not less than O(n). Even in the best case, the computational a large variety of fields, including self-driving cars [1], facial overhead increases linearly with DNN size, which recognition authorization [2], object detection [3], etc. is not suitable for buyers with limited computing resources. Training neural network models is expensive, which relies on Some researchers apply the selective encryption to reduce extensive datasets and computing resources. However, the resources the computational complexity of encryption and decryption of ordinary institutions or individuals are not always [8, 9]. In [8], the model can only be executed on trusted hardware.

We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sublinear (convex as well as positive homogeneous of degree one). Conversely, any sublinear function is the support function of a compact set. We leverage this property to transcribe the task of learning a compact set to that of learning its support function. We propose two algorithms to perform the sublinear regression, one via convex and another via nonconvex programming. The convex programming approach involves solving a quadratic program (QP). The nonconvex programming approach involves training a input sublinear neural network. We illustrate the proposed methods via numerical examples on learning the reach sets of controlled dynamics subject to set-valued input uncertainties from trajectory data.

Air Quality Multi-sensors Systems (AQMS) are IoT devices based on low cost chemical microsensors array that recently have showed capable to provide relatively accurate air pollutant quantitative estimations. Their availability permits to deploy pervasive Air Quality Monitoring (AQM) networks that will solve the geographical sparseness issue that affect the current network of AQ Regulatory Monitoring Systems (AQRMS). Unfortunately their accuracy have shown limited in long term field deployments due to negative influence of several technological issues including sensors poisoning or ageing, non target gas interference, lack of fabrication repeatability, etc. Seasonal changes in probability distribution of priors, observables and hidden context variables (i.e. non observable interferents) challenge field data driven calibration models which short to mid term performances recently rose to the attention of Urban authorithies and monitoring agencies. In this work, we address this non stationary framework with adaptive learning strategies in order to prolong the validity of multisensors calibration models enabling continuous learning. Relevant parameters influence in different network and note-to-node recalibration scenario is analyzed. Results are hence useful for pervasive deployment aimed to permanent high resolution AQ mapping in urban scenarios as well as for the use of AQMS as AQRMS backup systems providing data when AQRMS data are unavailable due to faults or scheduled mainteinance.