## 1 Introduction  
Governments are setting targets for carbon neutrality. The automotive industry is also under pressure to establish and significantly accelerate strategies for further improvements in energy efficiency and weight reduction toward zero greenhouse gas emissions. Meanwhile, a high level of comfort, which is achieved through quietness and good air-conditioning performance, among others, is needed to provide a safe, secure, pleasant traveling environment for customers. Porous sound-absorbing materials and porous thermal insulators are widely used to satisfy these requirements in a limited mass and space. A typical property that indicates the performance of a porous sound-absorbing material is its sound absorption coefficient. A high-performance porous sound absorber generally has a mixed structure of a solid phase as its base material and a fluid phase consisting of braided channels with diameters ranging from several tens of micrometers to several millimeters; its sound absorption properties depend on its microstructure [1; 2; 3; 4; 5]. Another typical property that arises from a porous structure is thermal conductivity. A high-performance porous thermal insulator generally has a mixed structure comprising a solid phase as its base material and a fluid phase consisting of independent spaces with diameters ranging from several tens of nanometers to several tens of micrometers; its thermal insulation properties also depend on its microstructure [6; 7; 8]. Thus, porous sound absorbers and porous thermal insulators are similar; they differ in the microstructures they offer for high performance, specifically the size and connectivity of their fluid phases. The difference in the size scale of the fluid phase makes it difficult to achieve compatibility between the two materials at high dimensions. Materials with excellent dual performance have been studied with experiments. Specifically, nanofibers and nanofiber-based composites have been investigated in the literature in the past decade. Materials such as polyacrylamide(PAN) [9], polyvinylidene fluoride [10], cellulose [11], polyurethane [12], and thermoplastic polyurethane (TPU)/polystyrene (PS) [13] were used either alone as nanofibers or as a part of composite for sound absorption properties. For example, [PERSON] et al. showed a thermal conductivity of 0.050 W/(m\(\cdot\)K) and a sound absorption coefficient of 0.5-0.6 around 1000 Hz with TPU/PS-BSE nanofibers fabricated with electrospinning solutions. [PERSON] et al. also summarized research trends in silica aerogel-based materials for acoustic applications [14]. For example, hot-pressed formed plates via the dry-mixing of silica aerogel with polyvinylbutyrate (PVB) showed a sound absorption coefficient of about 0.2 around 1000 Hz at a thickness of 10 mm. Polyethylene terephthalate (PET) nonwoven-silica aerogel blankets had a sound absorption coefficient of about 0.1 around 1000 Hz at a thickness of 5 mm. On the other hand, these studies point out the lack of mathematical modeling to understand key physical mechanisms that can explain the observed acoustical behavior of aerogels. Therefore, we have been working on the research and development of porous materials using materials model-based research through collaboration between industry, the government, and academia. This research method aims to develop materials with favorable performance efficiently by backcasting from the required functions of such products. The phenomena occurring in the internal microstructure of a material are modeled using mathematical formulas based on the energy propagation mechanism, and the product is designed based on the modeling results. We have developed a computational microstructure modeling approach that predicts three properties of porous materials: sound absorption, thermal insulation, and vibration damping (Figure 1) [15]. Vibration damping is an important property that affects the ride and feel of a vehicle, but it is not the subject of this study.